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One-dimensional topological theories with defects: the linear case. (English) Zbl 1532.18009

Im, Mee Seong (ed.) et al., Algebraic and topological aspects of representation theory. Virtual AMS special session on geometric and algebraic aspects of quantum groups and related topics, virtual, November 20–21, 2021. Providence, RI: American Mathematical Society (AMS). Contemp. Math. 791, 105-146 (2024).

Reviewer: Hirokazu Nishimura (Tsukuba)

MSC: 18M05 18M30 57K16 16W60 15A63

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Bell, Jason; Smertnig, Daniel

Noncommutative rational Pólya series. (English) Zbl 1515.68188

Sel. Math., New Ser. 27, No. 3, Paper No. 34, 34 p. (2021).

MSC: 68Q70 11D88 16W60 11D61

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OA License

Klep, Igor; Vinnikov, Victor; Volčič, Jurij

Local theory of free noncommutative functions: germs, meromorphic functions, and Hermite interpolation. (English) Zbl 1444.32003

Trans. Am. Math. Soc. 373, No. 8, 5587-5625 (2020).

MSC: 32A20 47A56 16W60 16R50 32A05 16K40

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Kaliuzhnyi-Verbovetskyi, Dmitry S.; Vinnikov, Victor

Noncommutative rational functions, their difference-differential calculus and realizations. (English) Zbl 1255.93073

Multidimensional Syst. Signal Process. 23, No. 1-2, 49-77 (2012).

MSC: 93C35 93B25

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Alpay, D.; Kaliuzhnyi-Verbovetzkyi, D. S.

Matrix-\(J\)-unitary non-commutative rational formal power series. (English) Zbl 1110.47008

Alpay, Daniel (ed.) et al., The state space method generalizations and applications. Basel: Birkhäuser (ISBN 3-7643-7370-9/hbk). Operator Theory: Advances and Applications 161, 49-113 (2006).

Reviewer: A. V. Balakrishnan (Los Angeles)

MSC: 47A48 13F25 46C20 46E22 93B20 93D05

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Sauer, Roman

Power series over the group ring of a free group and applications to Novikov-Shubin invariants. (English) Zbl 1051.16013

Farrell, F. T. (ed.) et al., High-dimensional manifold topology. Proceedings of the school, ICTP, Trieste, Italy, May 21–June 8, 2001. River Edge, NJ: World Scientific (ISBN 981-238-223-2/hbk). 449-468 (2003).

Reviewer: S. V. Mihovski (Plovdiv)

MSC: 16S34 16W60 46L51 30B10 57R20 46L10

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Minh, Hoang N.

Finite polyzêtas, poly-Bernoulli numbers, identities of polyzêtas and noncommutative rational power series. (English) Zbl 1067.11011

Harju, Tero (ed.) et al., Proceedings of WORDS’03, the 4th international conference on combinatorics on words, Turku, Finland, September 10–13, 2003. Turku: Turku Centre for Computer Science (ISBN 952-12-1211-X/pbk). TUCS General Publication 27, 232-250 (2003).

Reviewer: Jean-Paul Allouche (Orsay)

MSC: 11B99 33B30 33E20 11B68

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Houseaux, V.; Jacob, G.; Oussous, N. E.; Petitot, M.

Maple package for noncommutative rational power series. (English) Zbl 1195.11165

Li, Ziming (ed.) et al., Computer mathematics. Proceedings of the sixth Asian symposium (ASCM 2003), Beijing, China, April 17–19, 2003. River Edge, NJ: World Scientific (ISBN 981-238-220-8/hbk). Lect. Notes Ser. Comput. 10, 174-188 (2003).

MSC: 11Y16 11M32 65Y20 68W30

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Chan, Daniel

Noncommutative rational double points. (English) Zbl 0974.16022

J. Algebra 232, No. 2, 725-766 (2000).

Reviewer: Aleksandr G.Aleksandrov (Moskva)

MSC: 16S38 16S15 14J26 14M05 16W22 16W60 16E65 16G60 16G50

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Gelfand, Israel M.; Krob, Daniel; Lascoux, Alain; Leclerc, Bernard; Retakh, Vladimir S.; Thibon, Jean-Yves

Noncommutative symmetric functions. (English) Zbl 0831.05063

Adv. Math. 112, No. 2, 218-348 (1995).

Reviewer: V.A.Ufnarovski (Lund)

MSC: 05E05 05E10 15A09 15A15 41A21 68Q70 16W30

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Gerardin, Khyra

Quotient de Hadamard de séries rationnelles. (French) Zbl 0512.16003

Groupe Etude Anal. Ultrametrique 9e Annee: 1981/82, No. 2, Expose No. 20, 23 p. (1983).

MSC: 16W60 11B37 30B10

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Wechler, W.

Formal power series and (R,P)-rational languages. (English) Zbl 0486.68086

Mathematical models in computer systems, Proc. 3rd Hung. Comput. Sci. Conf., Budapest 1981, 43-54 (1981).

MSC: 68Q45 16W60 20M35

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Salomaa, Arto

Formal power series in noncommuting variables. (English) Zbl 0485.68076

18th Scand. Congr. Math., Proc., Aarhus 1980, Prog. Math. 11, 104-124 (1981).

MSC: 68Q45 16W60 68-02

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Platonov, V. P.; Yanchevskij, V. I.

\(SK_1\) for division rings of noncommutative rational functions. (English. Russian original) Zbl 0437.16015

Sov. Math., Dokl. 20, 1393-1397 (1979); translation from Dokl. Akad. Nauk SSSR 249, 1064-1068 (1979).

MSC: 16Kxx 16E20 16P10 16W60

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Fliess, Michel

Automates stochastiques et séries rationnelles non commutatives. (French) Zbl 0262.94038

Automata, Languages, Programming, Proc. Sympos. Inst. Rech. Informatique Automatique (IRIA), Rocquencourt 1972, 397-411 (1973).

Reviewer: Michel Fliess

MSC: 68Q45 16W60

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Fliess, Michel

Du produit de Hurwitz de deux séries formelles. (French) Zbl 0169.35904

C. R. Acad. Sci., Paris, Sér. A 268, 535-537 (1969).

Reviewer: Michel Fliess

MSC: 16-XX

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Found 16 Documents (Results 1–16)

One-dimensional topological theories with defects: the linear case. (English) Zbl 1532.18009

Noncommutative rational Pólya series. (English) Zbl 1515.68188

Local theory of free noncommutative functions: germs, meromorphic functions, and Hermite interpolation. (English) Zbl 1444.32003

Noncommutative rational functions, their difference-differential calculus and realizations. (English) Zbl 1255.93073

Matrix-\(J\)-unitary non-commutative rational formal power series. (English) Zbl 1110.47008

Power series over the group ring of a free group and applications to Novikov-Shubin invariants. (English) Zbl 1051.16013

Finite polyzêtas, poly-Bernoulli numbers, identities of polyzêtas and noncommutative rational power series. (English) Zbl 1067.11011

Maple package for noncommutative rational power series. (English) Zbl 1195.11165

Noncommutative rational double points. (English) Zbl 0974.16022

Noncommutative symmetric functions. (English) Zbl 0831.05063

Quotient de Hadamard de séries rationnelles. (French) Zbl 0512.16003

Formal power series and (R,P)-rational languages. (English) Zbl 0486.68086

Formal power series in noncommuting variables. (English) Zbl 0485.68076

\(SK_1\) for division rings of noncommutative rational functions. (English. Russian original) Zbl 0437.16015

Automates stochastiques et séries rationnelles non commutatives. (French) Zbl 0262.94038

Du produit de Hurwitz de deux séries formelles. (French) Zbl 0169.35904

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