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A retrospect of the research in nonassociative algebras in IME-USP. (English) Zbl 1502.17001

Summary: The aim of this paper is to give an overview of the participation of our research group in the development of nonassociative algebras.

MSC:

17-02 Research exposition (monographs, survey articles) pertaining to nonassociative rings and algebras
17-03 History of nonassociative rings and algebras
Full Text: DOI

References:

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[142] Mostovoy, J.; Pérez-Izquierdo, JM; Shestakov, IP, A non-associative Baker-Campbell-Hausdorff formula, Proc. Am. Math. Soc., 145, 12, 5109-5122 (2017) · Zbl 1428.17002
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[144] Murakami, LSI; Shestakov, IP, Irreducible unital right alternative bimodules, J. Algebra, 246, 2, 897-914 (2001) · Zbl 1002.17018
[145] Pchelintsev, SV; Shashkov, OV; Shestakov, I., Right alternative bimodules over Cayley algebra and coordinatization theorem, J. Algebra, 572, 111-128 (2021) · Zbl 1475.17052
[146] Pchelintsev, SV; Shestakov, I., Prime \((-1,1)\) and Jordan monsters and superalgebras of vector type, J. Algebra, 423, 54-86 (2015) · Zbl 1369.17029
[147] Pchelintsev, S.V., Shestakov, I.P.: Constants of partial derivations and primitive operations. Algebra Logika 56(3), 317-347 (2017). English translation: Algebra Logic 56(3), 210-231 (2017) · Zbl 1422.08001
[148] Peresi, LA, On baric algebras with prescribed automorphisms, Linear Algebra Appl., 78, 163-185 (1986) · Zbl 0586.17014
[149] Peresi, LA, A note on duplication of algebras, Linear Algebra Appl., 104, 65-69 (1988) · Zbl 0651.17013
[150] Peresi, LA, On derivations of baric algebras with prescribed automorphisms, Linear Algebra Appl., 104, 71-74 (1988) · Zbl 0651.17014
[151] Peresi, LA, Nilpotency in Bernstein algebras, Arch. Math. (Basel), 56, 5, 437-439 (1991) · Zbl 0692.17013
[152] Peresi, LA, A basis of identities for Bernstein algebras, Int. J. Math. Game Theory Algebra, 14, 3, 179-188 (2004) · Zbl 1092.17001
[153] Pérez-Izquierdo, JM; Shestakov, IP, An envelope for Malcev algebras, J. Algebra, 272, 1, 379-393 (2004) · Zbl 1077.17027
[154] Pérez-Izquierdo, J.M., Shestakov, I.P.: On the center of the universal enveloping algebra of the central simple non-Lie Malcev algebras in characteristic \(p\). In: Proceedings of Jordan Structures in Algebra and Analysis Meeting, pp. 227-242. Editorial Círculo Rojo, Almería (2010) · Zbl 1259.17026
[155] Pérez-Izquierdo, JM; Shestakov, IP, Co-Moufang deformations of the universal enveloping algebra of the algebra of traceless octonions, Algebr. Represent. Theory, 18, 5, 1247-1265 (2015) · Zbl 1395.17077
[156] Petrogradsky, VM, Examples of self-iterating Lie algebras, J. Algebra, 302, 2, 881-886 (2006) · Zbl 1109.17008
[157] Petrogradsky, VM; Shestakov, IP, Examples of self-iterating Lie algebras, II. J. Lie Theory, 19, 4, 697-724 (2009) · Zbl 1253.17011
[158] Petrogradsky, VM; Shestakov, IP; Zelmanov, E., Nil graded self-similar algebras, Groups Geom. Dyn., 4, 4, 873-900 (2010) · Zbl 1229.17025
[159] Picanço, J.; Murakami, SL; Shestakov, IP, On right alternative superalgebras, Commun. Algebra, 44, 1, 240-252 (2016) · Zbl 1384.17007
[160] Pozhidaev, A.P., Shestakov, I.P.: Noncommutative Jordan superalgebras of degree n > 2. Algebra Logika 49(1), 26-59, 149-150, 152-153 (2010). English translation: Algebra Logic 49(1), 18-42 (2010) · Zbl 1195.17025
[161] Pozhidaev, A.P., Shestakov, I.P.: Noncommutative Jordan superalgebras of degree \(n\ge 2\). Dokl. Akad. Nauk 431(2), 165-169 (2010). English translation: Dokl. Math. 81(2), 204-208 (2010) · Zbl 1219.17001
[162] Pozhidaev, AP; Shestakov, IP, Structurable superalgebras of Cartan type, J. Algebra, 323, 12, 3230-3251 (2010) · Zbl 1201.17013
[163] Pozhidaev, A.P., Shestakov, I.P.: Structurable superalgebras of Cartan type. Dokl. Akad. Nauk 432(2), 167-173 (2010). English translation: Dokl. Math. 81(3), 373-378 (2010) · Zbl 1238.17004
[164] Pozhidaev, A.P., Shestakov, I.P.: Simple finite-dimensional noncommutative Jordan superalgebras of characteristic 0. Sibirsk. Mat. Zh. 54(2), 389-406 (2013). English translation: Sib. Math. J. 54(2), 301-316 (2013) · Zbl 1276.17017
[165] Pozhidaev, AP; Shestakov, IP, Simple finite-dimensional modular noncommutative Jordan superalgebras, J. Pure Appl. Algebra, 223, 6, 2320-2344 (2019) · Zbl 1472.17003
[166] Reed, ML, Algebraic structure of genetic inheritance, Bull. Am. Math. Soc. (N.S.), 34, 2, 107-130 (1997) · Zbl 0876.17040
[167] Romanovskiĭ, N.S., Shestakov, I.P.: Equational Noetherianity of the universal enveloping algebra of wreath products of abelian Lie algebras. Algebra Logika 47(4), 475-490, 525 (2008). English translation: Algebra Logic 47(4), 269-278 (2008) · Zbl 1164.17010
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[169] Shchigolev, V.V.: Construction of non-finitely based T-ideals, vol. 29, pp. 3935-3941 (2001). Special issue dedicated to Alexei Ivanovich Kostrikin · Zbl 0999.16020
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[171] Shestakov, I.P.: Prime alternative superalgebras of arbitrary characteristic. Algebra i Logika 36(6), 675-716, 722 (1997). English translation: Algebra Logic 36(6), 389-41 (1997) · Zbl 0904.17025
[172] Shestakov, IP, Every Akivis algebra is linear, Geom. Dedicata, 77, 2, 215-223 (1999) · Zbl 1043.17002
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[174] Shestakov, IP, Moufang loops and alternative algebras, Proc. Am. Math. Soc., 132, 2, 313-316 (2004) · Zbl 1038.17024
[175] Shestakov, IP, On speciality of Jordan brackets, Algebra Discrete Math., 3, 94-101 (2009) · Zbl 1185.17024
[176] Shestakov, I.P.: Associative identities of octonions. Algebra Logika 49(6), 834-839, 846, 849 (2010). English translation: Algebra Logic 49(6), 561-565 (2011) · Zbl 1248.17002
[177] Shestakov, I.P.: On commuting U-operators in Jordan algebras. In: Non-associative and Non-commutative Algebra and Operator Theory, Volume 160 of Springer Proc. Math. Stat., pp. 105-109. Springer, Cham (2016) · Zbl 1378.17048
[178] Shestakov, IP, Skew-symmetric identities of finitely generated malcev algebras, Matematicheskii Zhurnal, 132, 2, 206-213 (2016) · Zbl 1479.17059
[179] Shestakov, IP; Kornev, AI, On the radical of a free Malcev algebra, Proc. Am. Math. Soc., 140, 9, 3049-3054 (2012) · Zbl 1301.17021
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[181] Shestakov, IP; Trushina, M., Irreducible bimodules over alternative algebras and superalgebras, Trans. Am. Math. Soc., 368, 7, 4657-4684 (2016) · Zbl 1397.17006
[182] Shestakov, IP; Tsurkov, A., Automorphic equivalence of the representations of Lie algebras, Algebra Discrete Math., 15, 1, 96-126 (2013) · Zbl 1358.17010
[183] Shestakov, IP; Umirbaev, UU, Free Akivis algebras, primitive elements, and hyperalgebras, J. Algebra, 250, 2, 533-548 (2002) · Zbl 0993.17002
[184] Shestakov, IP; Umirbaev, UU, The Nagata automorphism is wild, Proc. Natl. Acad. Sci. USA, 100, 22, 12561-12563 (2003) · Zbl 1065.13010
[185] Shestakov, IP; Umirbaev, UU, Poisson brackets and two-generated subalgebras of rings of polynomials, J. Am. Math. Soc., 17, 1, 181-196 (2004) · Zbl 1044.17014
[186] Shestakov, IP; Umirbaev, UU, The tame and the wild automorphisms of polynomial rings in three variables, J. Am. Math. Soc., 17, 1, 197-227 (2004) · Zbl 1056.14085
[187] Shestakov, IP; Zaicev, M., Polynomial identities of finite dimensional simple algebras, Commun. Algebra, 39, 3, 929-932 (2011) · Zbl 1253.17003
[188] Shestakov, IP; Zelmanov, E., Some examples of nil Lie algebras, J. Eur. Math. Soc. (JEMS), 10, 2, 391-398 (2008) · Zbl 1144.17013
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[192] Shestakov, IP; Zhukavets, N., The free alternative superalgebra on one odd generator, Internat. J. Algebra Comput., 17, 5-6, 1215-1247 (2007) · Zbl 1205.17033
[193] Shestakov, IP; Zhukavets, N., Skew-symmetric identities of octonions, J. Pure Appl. Algebra, 213, 4, 479-492 (2009) · Zbl 1241.17033
[194] Solarte, OF; Shestakov, IP, Irreductible representations of the simple Jordan superalgebra of Grassmann Poisson bracket, J. Algebra, 455, 291-313 (2016) · Zbl 1344.17026
[195] Veloso, M.; Shestakov, IP, Rings of constants of linear derivations on Fermat rings, Commun. Algebra, 46, 12, 5469-5479 (2018) · Zbl 1461.13031
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[198] Zhelyabin, V.N., Shestakov, I.P.: Chevalley and Kostant theorems for Malcev algebras. Algebra Logika 46(5), 560-584, 664 (2007). English translation: Algebra Logic 46(5), 303-317 (2007) · Zbl 1164.17025
[199] Zhukavets, N., Shestakov, I.P.: A base of the free alternative superalgebra on one odd generator. Dokl. Akad. Nauk 422(2), 169-171 (2008). English translation: Dokl. Math. 78(2), 693-695 (2008) · Zbl 1216.17003
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