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 Sibirsk. Mat. Zh., 2017, Volume 58, Number 4, Pages 894–915 (Mi smj2907)

Identities of metabelian alternative algebras

S. V. Pchelintsevab

a Financial University Under the Government of the Russian Federation Moscow, Russia
b Sobolev Institute of Mathematics, Novosibirsk, Russia

Abstract: We study metabelian alternative (in particular, associative) algebras over a field of characteristic 0. We construct additive bases of the free algebras of mentioned varieties, describe some centers of these algebras, compute the values of the sequence of codimensions of corresponding $T$-ideals, and find unitarily irreducible components of the decomposition of mentioned varieties into a union and their bases of identities. In particular, we find a basis of identities for the metabelian alternative Grassmann algebra. We prove that the free algebra of a variety that is generated by the metabelian alternative Grassmann algebra possesses the zero associative center.

Keywords: free algebra, metabelian algebra, center of an algebra, sequence of codimensions of a Tideal, union of varieties.

 Funding Agency Grant Number Russian Foundation for Basic Research 16-01-00756 The author was supported by the Russian Foundation for Basic Research (Grant 16-01-00756).

DOI: https://doi.org/10.17377/smzh.2017.58.416

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English version:
Siberian Mathematical Journal, 2017, 58:4, 693–710

Bibliographic databases:

UDC: 512.552.5+512.572
MSC: 35R30

Citation: S. V. Pchelintsev, “Identities of metabelian alternative algebras”, Sibirsk. Mat. Zh., 58:4 (2017), 894–915; Siberian Math. J., 58:4 (2017), 693–710

Citation in format AMSBIB
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Citing articles on Google Scholar: Russian citations, English citations
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This publication is cited in the following articles:
1. A. V. Grishin, “Asymptotics of the Codimensions $c_n$ in the Algebra $F^{(7)}$”, Math. Notes, 104:1 (2018), 22–28
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