Structure of the Variety of Alternative Algebras with the Lie-Nilpotency Identity of Degree 5

被引：0

作者：

S. V. Pchelintsev

机构：

[1] Financial University under the Government of the Russian Federation,

[2] St. Petersburg State University,undefined

来源：

Siberian Mathematical Journal | 2024年 / 65卷

关键词：

Lie-nilpotent algebra; alternative algebra; codimension of a T-ideal; additive basis for a free algebra; center of an algebra; 512.554;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

We construct an additive basis for a relatively free alternative algebra of Lie-nilpotent degree 5, describe the associative center and core of this algebra, and find the T-generators of the full center. Also, we give some asymptotic estimate for the codimension of the T-ideal generated by a commutator of degree 5 in a free alternative algebra, and find a finite-dimensional superalgebra that generates the variety of alternative algebras with the Lie-nilpotency of the selfadjoint operator of degree 5.

引用

页码：139 / 152

页数：13

共 16 条

[1]

Grishin AV(2015)On centers of relatively free associative algebras with a Lie nilpotency identity Sb. Math. 206 1610-1627

[2]

Pchelintsev SV(2016)Proper central and core polynomials of relatively free associative algebras with identity of Lie nilpotency of degrees 5 and 6 Sb. Math. 207 674-692

[3]

Grishin AV(2018)Identities of the model algebra of multiplicity 2 Sib. Math. J. 59 1103-1124

[4]

Pchelintsev SV(2020)Construction and applications of an additive basis for the relatively free associative algebra with the Lie nilpotency identity of degree 5 Sib. Math. J. 61 139-153

[5]

Pchelintsev SV(2017)Identities of metabelian alternative algebras Sib. Math. J. 58 693-710

[6]

Pchelintsev SV(2023)Product theorems for alternative algebras and some of their applications Sib. Math. J. 64 374-392

[7]

Pchelintsev SV(1961)Malcev algebras Trans. Amer. Math. Soc. 101 426-458

[8]

Pchelintsev SV(2007)The free alternative superalgebra on one odd generator Internat. J. Algebra Comput. 17 1215-1247

[9]

Sagle AA(2003)A free alternative algebra with the identity Chebyshevskii Sb. (Tula) 4 54-60

[10]

Shestakov IP(1985)Varieties and Math. USSR-Izv. 25 359-374

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