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Krichever-Novikov type algebras. A general review and the genus zero case. (English) Zbl 07619843

Hervik, Sigbjørn (ed.) et al., Geometry, Lie theory and applications. Proceedings of the Abel symposium 2019, Ålesund, Norway June 24–28, 2019. Cham: Springer. Abel Symp. 16, 279-330 (2022).

Reviewer: Alice Fialowski (Budapest)

MSC: 17B66 17B56 17B65 17B68 30F30 81T40

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Futorny, Vyacheslav

Representations of Lie algebras. (English) Zbl 1512.17008

São Paulo J. Math. Sci. 16, No. 1, 131-156 (2022).

Reviewer: Mee Seong Im (Annapolis)

MSC: 17B10 17-02 17B65 17B67

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Zuevsky, A.

Characterization of codimension one foliations on complex curves by connections. (English) Zbl 1487.32123

Rev. Math. Phys. 34, No. 3, Article ID 2230002, 50 p. (2022).

MSC: 32M25 32S65 37F75

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Albino dos Santos, Felipe

On the universal central extension of superelliptic affine Lie algebras. (English) Zbl 1508.17007

Commun. Algebra 50, No. 5, 2045-2055 (2022).

Reviewer: Alice Fialowski (Budapest)

MSC: 17B05 17B65

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Honda, Masaki; Sato, Matsuo; Tohshima, Taiki

Superstring backgrounds in string geometry. (English) Zbl 1473.81137

Adv. High Energy Phys. 2021, Article ID 9993903, 7 p. (2021); erratum ibid. 2022, Article ID 9768247, 1 p. (2022).

MSC: 81T30 81V17 83C45

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Barnich, Glenn; Ruzziconi, Romain

Coadjoint representation of the BMS group on celestial Riemann surfaces. (English) Zbl 1466.81028

J. High Energy Phys. 2021, No. 6, Paper No. 79, 41 p. (2021).

MSC: 81R05 83C05 53Z05

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Sheinman, Oleg

Quantization of Lax integrable systems and conformal field theory. (English) Zbl 1464.81049

Fialowski, Alice (ed.) et al., Homotopy algebras, deformation theory and quantization. Selected papers based on the presentations at the conference, September 16 and 22, 2018, Poznań, Poland. Warsaw: Polish Academy of Sciences, Institute of Mathematics. Banach Cent. Publ. 123, 111-122 (2021).

MSC: 81T40 14H70 81R12 81S10 53D50 37K20 81T70

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Schlichenmaier, Martin

Krichever-Novikov type algebras: definitions and results. (English) Zbl 1496.17019

Makhlouf, Abdenacer (ed.), Algebra and applications 1. Non-associative algebras and categories. Sciences. Mathematics. London: ISTE; Hoboken, NJ: John Wiley & Sons. 199-244 (2020).

Reviewer: Alice Fialowski (Budapest)

MSC: 17B68

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Sheinman, O. K.

Quantization of integrable systems with spectral parameter on a Riemann surface. (English. Russian original) Zbl 1502.37062

Dokl. Math. 102, No. 3, 524-527 (2020); translation from Dokl. Ross. Akad. Nauk, Mat. Inform. Protsessy Upr. 495, 91-94 (2020).

MSC: 37J37 37J35 14H70 53D55 81T40 81T70

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Sato, Matsuo; Sugimoto, Yuji

Topological string geometry. (English) Zbl 1473.81145

Nucl. Phys., B 956, Article ID 115019, 20 p. (2020).

MSC: 81T30 81T45 81T16

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Sato, Matsuo

String geometry and nonperturbative formulation of string theory. (English) Zbl 1471.81079

Int. J. Mod. Phys. A 34, No. 23, Article ID 1950126, 22 p. (2019).

MSC: 81T30 81T60 81T16 14D22 14H55 81U05

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Grushevsky, S.; Krichever, I. M.; Norton, C.

Real-normalized differentials: limits on stable curves. (English. Russian original) Zbl 1437.14033

Russ. Math. Surv. 74, No. 2, 265-324 (2019); translation from Usp. Mat. Nauk 74, No. 2, 81-148 (2019).

Reviewer: Dawei Chen (Chestnut Hill)

MSC: 14H10 14H15 30F30 32G15

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Liu, Dong; Pei, Yufeng; Xia, Limeng

Representations for three-point Lie algebras of genus zero. (English) Zbl 1461.17024

Int. J. Math. 30, No. 14, Article ID 1950070, 17 p. (2019).

MSC: 17B65 17B68 17B69

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Futorny, Vyacheslav; Kochloukova, Dessislava H.; Sidki, Said N.

On self-similar Lie algebras and virtual endomorphisms. (English) Zbl 1472.17065

Math. Z. 292, No. 3-4, 1123-1156 (2019).

Reviewer: Victor Petrogradsky (Brasília)

MSC: 17B50 17B05 17B60 17B66

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Cox, Ben; Jurisich, Elizabeth; Martins, Renato A.

The three point gauge algebra \(\mathcal{V} \ltimes \mathfrak{sl}(2, \mathcal{R}) \oplus(\Omega_{\mathcal{R}} / d \mathcal{R})\) and its action on a Fock space. (English) Zbl 1462.17026

J. Algebra 521, 44-64 (2019).

Reviewer: Stefano Capparelli (Roma)

MSC: 17B67 81R10

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Cox, Ben; Zhao, Kaiming

Certain families of polynomials arising in the study of hyperelliptic Lie algebras. (English) Zbl 1436.17031

Ramanujan J. 46, No. 2, 323-344 (2018).

MSC: 17B65 14H55 42C10

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Grinevich, Petr G.; Novikov, Sergei P.

Singular solitons and spectral meromorphy. (English. Russian original) Zbl 1407.34123

Russ. Math. Surv. 72, No. 6, 1083-1107 (2017); translation from Usp. Mat. Nauk 72, No. 6, 113-138 (2017).

Reviewer: Hubert Kalf (München)

MSC: 34M05 34L40 47B50

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Sheĭnman, O. K.

Almost graded current algebras on the symmetric square of a curve. (English. Russian original) Zbl 1448.17025

Russ. Math. Surv. 72, No. 2, 384-386 (2017); translation from Usp. Mat. Nauk 72, No. 2, 197-198 (2017).

MSC: 17B65 17B70 14J99

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Cox, Ben; Guo, Xiangqian; Lu, Rencai; Zhao, Kaiming

Simple superelliptic Lie algebras. (English) Zbl 1418.17016

Commun. Contemp. Math. 19, No. 3, Article ID 1650032, 22 p. (2017).

MSC: 17B05 17B20 17B40 17B60 14H55

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Pei, Yufeng; Sun, Jiancai

Vertex algebras associated to a class of Lie algebras of Krichever-Novikov type. (English) Zbl 1350.17017

J. Geom. Phys. 110, 176-186 (2016).

MSC: 17B69 17B68

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Cox, Ben

Module structure of the center of the universal central extension of a genus zero Krichever-Novikov algebra. (English) Zbl 1395.17048

J. Algebra 467, 58-79 (2016).

MSC: 17B67 81R10 81T40

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Cox, Ben

On the universal central extension of hyperelliptic current algebras. (English) Zbl 1383.17012

Proc. Am. Math. Soc. 144, No. 7, 2825-2835 (2016).

MSC: 17B65 17B56

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Freidel, Laurent; Leigh, Robert G.; Minic, Djordje

Metastring theory and modular space-time. (English) Zbl 1388.81528

J. High Energy Phys. 2015, No. 6, Paper No. 6, 76 p. (2015).

MSC: 81T30 83E30 81T20

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Cox, Ben; Futorny, Vyacheslav; Martins, Renato Alessandro

Free field realizations of the Date-Jimbo-Kashiwara-Miwa algebra. (English) Zbl 1391.17023

Mason, Geoffrey (ed.) et al., Developments and retrospectives in Lie theory. Algebraic methods. Retrospective selected papers based on the presentations at the seminar “Lie groups, Lie algebras and their representations”, 1991–2014. Cham: Springer (ISBN 978-3-319-09803-6/hbk; 978-3-319-09804-3/ebook). Developments in Mathematics 38, 111-136 (2014).

MSC: 17B65 17B69

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Anguelova, Iana I.

Virasoro structures in the twisted vertex algebra of the particle correspondence of type C. (English) Zbl 1317.81150

Dobrev, Vladimir (ed.), Lie theory and its applications in physics. Selected papers based on the presentations at the 10th international workshop, LT 10, Varna, Bulgaria, June 17–23, 2013. Tokyo: Springer (ISBN 978-4-431-55284-0/hbk; 978-4-431-55285-7/ebook). Springer Proceedings in Mathematics & Statistics 111, 435-446 (2014).

MSC: 81R10 81V25 14D21 17B69 17B81

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Schlichenmaier, Martin

From the Virasoro algebra to Krichever-Novikov type algebras and beyond. (English) Zbl 1369.17023

Vasil’ev, Alexander (ed.), Harmonic and complex analysis and its applications. Cham: Birkhäuser/Springer (ISBN 978-3-319-01805-8/hbk; 978-3-319-01806-5/ebook). Trends in Mathematics, 325-358 (2014).

MSC: 17B68 17B65

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Anguelova, Iana I.

Boson-fermion correspondence of type D-A and multi-local Virasoro representations on the Fock space \( {F^{\otimes \frac{1}{2}}}\). (English) Zbl 1307.82015

J. Math. Phys. 55, No. 11, 111704, 23 p. (2014).

Reviewer: Guy Jumarie (Montréal)

MSC: 82C22 81R15 81R10 17B68

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Cox, Ben; Futorny, Vyacheslav; Tirao, Juan A.

DJKM algebras and non-classical orthogonal polynomials. (English) Zbl 1302.17034

J. Differ. Equations 255, No. 9, 2846-2870 (2013).

Reviewer: Volodymyr Mazorchuk (Uppsala)

MSC: 17B65 33C45 34A05

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Schlichenmaier, Martin

Lie superalgebras of Krichever-Novikov type and their central extensions. (English) Zbl 1376.17029

Anal. Math. Phys. 3, No. 3, 235-261 (2013).

MSC: 17B56 17B65 17B68 17B66 30F30 81R10 81T40

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Kreusch, Marie

Extensions of superalgebras of Krichever-Novikov type. (English) Zbl 1366.17023

Lett. Math. Phys. 103, No. 11, 1171-1189 (2013).

MSC: 17B66 17B68 17B56

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Wagemann, Friedrich

More remarks on the cohomology of Krichever-Novikov algebras. (English) Zbl 1307.17025

Afr. Mat. 23, No. 1, 41-52 (2012).

MSC: 17B56 17B68 32C18 32M25

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Sheinman, O. K.

Krichever-Novikov algebras, their representations and applications in geometry and mathematical physics. (English. Russian original) Zbl 1330.17031

Proc. Steklov Inst. Math. 274, Suppl. 1, S85-S161 (2011); translation from Sovrem. Probl. Mat. 10, 5-140 (2007).

MSC: 17B68 17B81 81R10 14D21 17B10 22E47 37K20

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Bueno, André; Cox, Ben; Futorny, Vyacheslav

Free field realizations of the elliptic affine Lie algebra \(\mathfrak{sl}(2, \mathbb R)\oplus (\varOmega_R/dR)\). (English) Zbl 1217.17015

J. Geom. Phys. 59, No. 9, 1258-1270 (2009).

Reviewer: Volodymyr Mazorchuk (Uppsala)

MSC: 17B67 81R10

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Krichever, I. M.; Sheinman, O. K.

Lax operator algebras. (English. Russian original) Zbl 1160.17017

Funct. Anal. Appl. 41, No. 4, 284-294 (2007); translation from Funkts. Anal. Prilozh. 41, No. 4, 46-59 (2007).

Reviewer: Nicolás Andruskiewitsch (Cordoba)

MSC: 17B65 14H70 14H60

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Donin, Dmitry; Khesin, Boris

Pseudodifferential symbols on Riemann surfaces and Krichever-Novikov algebras. (English) Zbl 1140.17019

Commun. Math. Phys. 272, No. 2, 507-527 (2007).

Reviewer: Friedrich Wagemann (Nantes)

MSC: 17B68 17B66 17B62 32G34 37K10 37K30

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Fialowski, A.; Schlichenmaier, M.

Global geometric deformations of the Virasoro algebra, current and affine algebras by Krichever-Novikov type algebras. (English) Zbl 1127.81021

Int. J. Theor. Phys. 46, No. 11, 2708-2724 (2007).

MSC: 17B68 81T40 81T10

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Inoguchi, J.; Toda, M.

Timelike minimal surfaces via loop groups. (English) Zbl 1185.53008

Acta Appl. Math. 83, No. 3, 313-355 (2004).

MSC: 53A10 58E20 22E67

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Bandelloni, G.; Lazzarini, S.

Primary currents and Riemannian geometry in W algebras. (English) Zbl 0969.81600

Nucl. Phys., B 606, No. 3, 673-688 (2001).

MSC: 81T20

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Ferrari, Franco; Sobczyk, Jan

Bosonic field propagators on algebraic curves. (English) Zbl 0978.81068

J. Math. Phys. 41, No. 9, 6444-6462 (2000).

MSC: 81T30 14H81 81T40 82D20

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Grinevich, P. G.; Schmidt, M. U.

Conformal invariant functionals of immersions of tori into \(\mathbb{R}^3\). (English) Zbl 0949.53007

J. Geom. Phys. 26, No. 1-2, 51-78 (1998).

MSC: 53A10 37K25 53C42 37J35

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Sheinman, O. K.

Orbits and representation of Krichever-Novikov affine-type algebras. (English) Zbl 0890.17026

J. Math. Sci., New York 82, No. 6, 3834-3843 (1996).

Reviewer: M.Schlichenmaier (Mannheim)

MSC: 17B67 14H55 81R10 22E67 30F30 81T40

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Sheinman, O. K.

Modules with highest weight for affine Lie algebras on Riemann surfaces. (English. Russian original) Zbl 0848.17023

Funct. Anal. Appl. 29, No. 1, 44-55 (1995); translation from Funkts. Anal. Prilozh. 29, No. 1, 56-71 (1995).

Reviewer: M.Schlichenmaier (Mannheim)

MSC: 17B67 22E67 30F30 14H55

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Zucchini, Roberto

The Drinfeld-Sokolov holomorphic bundle and classical \(W\) algebras on Riemann surfaces. (English) Zbl 0824.32009

J. Geom. Phys. 16, No. 3, 237-274 (1995).

MSC: 32L81 32L05 81T40

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Deck, Thomas

Classical string dynamics with non-trivial topology. (English) Zbl 0830.53050

J. Geom. Phys. 16, No. 1, 1-14 (1995).

Reviewer: H.Rumpf (Wien)

MSC: 53C50 83E30 81T30

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Deck, Thomas

A geometric Cauchy problem for timelike minimal surfaces. (English) Zbl 0830.53049

Ann. Global Anal. Geom. 12, No. 4, 305-312 (1994).

Reviewer: H.Rumpf (Wien)

MSC: 53C42 81T30 53C50 35L70 83E30 58J47

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Aldrovandi, E.; Bonora, L.

Liouville and Toda field theories on Riemann surfaces. (English) Zbl 0825.14002

J. Geom. Phys. 14, No. 1, 65-109 (1994).

MSC: 14H55

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Sadov, V. A.

Bases on multipunctured Riemann surfaces and interacting strings amplitudes. (English) Zbl 0725.30033

Commun. Math. Phys. 136, No. 3, 585-597 (1991).

Reviewer: N.Jacob (Erlangen)

MSC: 30F99 81T40 81T30

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Sheĭnman, O. K.

Elliptic affine Lie algebras. (English. Russian original) Zbl 0715.17023

Funct. Anal. Appl. 24, No. 3, 210-219 (1990); translation from Funkts. Anal. Prilozh. 24, No. 3, 51-61 (1990).

Reviewer: Nicolás Andruskiewitsch

MSC: 17B65 17B68 14H52

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Klimek, Slawomir; Lesniewski, Andrzej

Global Laurent expansions on Riemann surfaces. (English) Zbl 0897.30019

Commun. Math. Phys. 125, No. 4, 597-611 (1989).

MSC: 30F30 14H55 32G15

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Sheĭnman, O. K.

Hamiltonian string formalism and discrete groups. (English. Russian original) Zbl 0711.58028

Funct. Anal. Appl. 23, No. 2, 124-128 (1989); translation from Funkts. Anal. Prilozh. 23, No. 2, 49-54 (1989).

Reviewer: V. Müller

MSC: 81T99 22E40 32G20 37N99 81T30 83E30

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Bonora, L.; Matone, M.; Rinaldi, M.

Relation between represenations of KN and Virasoro algebras. (English) Zbl 0689.17014

Phys. Lett. B 216, No. 3-4, 313-319 (1989).

MSC: 17B65 81T40 17B10 81R10

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Krichever, I. M.; Novikov, S. P.

Algebras of Virasoro type, energy-momentum tensor, and decomposition operators on Riemann surfaces. (English. Russian original) Zbl 0684.17012

Funct. Anal. Appl. 23, No. 1, 19-33 (1989); translation from Funkts. Anal. Prilozh. 23, No. 1, 24-40 (1989).

Reviewer: V.Pestov

MSC: 17B65 81Q30 81S10 81T60 30F99 17B67

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Zachos, Cosmas K.

Fermionic center in the superconformal algebra on the supertorus. (English) Zbl 0957.17507

Nucl. Phys., B, Proc. Suppl. 11, 414-424 (1989).

MSC: 17B68 14M30

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Bonora, L.; Bregola, M.; Cotta-Ramusino, P.; Martellini, M.

Virasoro-type algebras and BRST operators on Riemann surfaces. (English) Zbl 0717.17002

Phys. Lett. B. 205, No. 1, 53-56 (1988).

MSC: 17A45 58A50 81R99 30F99 17B68

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Krichever, I. M.; Novikov, S. P.

Virasoro-Gelfand-Fuks type algebras, Riemann surfaces, operator’s theory of closed strings. (English) Zbl 0707.17015

J. Geom. Phys. 5, No. 4, 631-661 (1988).

Reviewer: A.N.Pressley

MSC: 17B68 30F10 81T10 81T30

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Alberty, José; Taormina, Anne; van Baal, Pierre

Relating Kac-Moody, Virasoro and Krichever-Novikov algebras. (English) Zbl 0665.17011

Commun. Math. Phys. 120, No. 2, 249-260 (1988).

Reviewer: A.N.Pressley

MSC: 17B65 17B67 30F10 81T40 81T30

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Found 56 Documents (Results 1–56)

Krichever-Novikov type algebras. A general review and the genus zero case. (English) Zbl 07619843

Representations of Lie algebras. (English) Zbl 1512.17008

Characterization of codimension one foliations on complex curves by connections. (English) Zbl 1487.32123

On the universal central extension of superelliptic affine Lie algebras. (English) Zbl 1508.17007

Superstring backgrounds in string geometry. (English) Zbl 1473.81137

Coadjoint representation of the BMS group on celestial Riemann surfaces. (English) Zbl 1466.81028

Quantization of Lax integrable systems and conformal field theory. (English) Zbl 1464.81049

Krichever-Novikov type algebras: definitions and results. (English) Zbl 1496.17019

Quantization of integrable systems with spectral parameter on a Riemann surface. (English. Russian original) Zbl 1502.37062

Topological string geometry. (English) Zbl 1473.81145

String geometry and nonperturbative formulation of string theory. (English) Zbl 1471.81079

Real-normalized differentials: limits on stable curves. (English. Russian original) Zbl 1437.14033

Representations for three-point Lie algebras of genus zero. (English) Zbl 1461.17024

On self-similar Lie algebras and virtual endomorphisms. (English) Zbl 1472.17065

The three point gauge algebra \(\mathcal{V} \ltimes \mathfrak{sl}(2, \mathcal{R}) \oplus(\Omega_{\mathcal{R}} / d \mathcal{R})\) and its action on a Fock space. (English) Zbl 1462.17026

Certain families of polynomials arising in the study of hyperelliptic Lie algebras. (English) Zbl 1436.17031

Singular solitons and spectral meromorphy. (English. Russian original) Zbl 1407.34123

Almost graded current algebras on the symmetric square of a curve. (English. Russian original) Zbl 1448.17025

Simple superelliptic Lie algebras. (English) Zbl 1418.17016

Vertex algebras associated to a class of Lie algebras of Krichever-Novikov type. (English) Zbl 1350.17017

Module structure of the center of the universal central extension of a genus zero Krichever-Novikov algebra. (English) Zbl 1395.17048

On the universal central extension of hyperelliptic current algebras. (English) Zbl 1383.17012

Metastring theory and modular space-time. (English) Zbl 1388.81528

Free field realizations of the Date-Jimbo-Kashiwara-Miwa algebra. (English) Zbl 1391.17023

Virasoro structures in the twisted vertex algebra of the particle correspondence of type C. (English) Zbl 1317.81150

From the Virasoro algebra to Krichever-Novikov type algebras and beyond. (English) Zbl 1369.17023

Boson-fermion correspondence of type D-A and multi-local Virasoro representations on the Fock space \( {F^{\otimes \frac{1}{2}}}\). (English) Zbl 1307.82015

DJKM algebras and non-classical orthogonal polynomials. (English) Zbl 1302.17034

Lie superalgebras of Krichever-Novikov type and their central extensions. (English) Zbl 1376.17029

Extensions of superalgebras of Krichever-Novikov type. (English) Zbl 1366.17023

More remarks on the cohomology of Krichever-Novikov algebras. (English) Zbl 1307.17025

Krichever-Novikov algebras, their representations and applications in geometry and mathematical physics. (English. Russian original) Zbl 1330.17031

Free field realizations of the elliptic affine Lie algebra \(\mathfrak{sl}(2, \mathbb R)\oplus (\varOmega_R/dR)\). (English) Zbl 1217.17015

Lax operator algebras. (English. Russian original) Zbl 1160.17017

Pseudodifferential symbols on Riemann surfaces and Krichever-Novikov algebras. (English) Zbl 1140.17019

Global geometric deformations of the Virasoro algebra, current and affine algebras by Krichever-Novikov type algebras. (English) Zbl 1127.81021

Timelike minimal surfaces via loop groups. (English) Zbl 1185.53008

Primary currents and Riemannian geometry in W algebras. (English) Zbl 0969.81600

Bosonic field propagators on algebraic curves. (English) Zbl 0978.81068

Conformal invariant functionals of immersions of tori into \(\mathbb{R}^3\). (English) Zbl 0949.53007

Orbits and representation of Krichever-Novikov affine-type algebras. (English) Zbl 0890.17026

Modules with highest weight for affine Lie algebras on Riemann surfaces. (English. Russian original) Zbl 0848.17023

The Drinfeld-Sokolov holomorphic bundle and classical \(W\) algebras on Riemann surfaces. (English) Zbl 0824.32009

Classical string dynamics with non-trivial topology. (English) Zbl 0830.53050

A geometric Cauchy problem for timelike minimal surfaces. (English) Zbl 0830.53049

Liouville and Toda field theories on Riemann surfaces. (English) Zbl 0825.14002

Bases on multipunctured Riemann surfaces and interacting strings amplitudes. (English) Zbl 0725.30033

Elliptic affine Lie algebras. (English. Russian original) Zbl 0715.17023

Global Laurent expansions on Riemann surfaces. (English) Zbl 0897.30019

Hamiltonian string formalism and discrete groups. (English. Russian original) Zbl 0711.58028

Relation between represenations of KN and Virasoro algebras. (English) Zbl 0689.17014

Algebras of Virasoro type, energy-momentum tensor, and decomposition operators on Riemann surfaces. (English. Russian original) Zbl 0684.17012

Fermionic center in the superconformal algebra on the supertorus. (English) Zbl 0957.17507

Virasoro-type algebras and BRST operators on Riemann surfaces. (English) Zbl 0717.17002

Virasoro-Gelfand-Fuks type algebras, Riemann surfaces, operator’s theory of closed strings. (English) Zbl 0707.17015

Relating Kac-Moody, Virasoro and Krichever-Novikov algebras. (English) Zbl 0665.17011

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