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.
This publication is cited in the following 4 articles:
S. V. Pchelintsev, “Structure of the Variety of Alternative Algebras with the Lie-Nilpotency Identity of Degree 5”, Sib Math J, 65:1 (2024), 139
S. V. Pchelintsev, “Stroenie mnogoobraziya alternativnykh algebr s tozhdestvom Li-nilpotentnosti stepeni 5”, Sib. matem. zhurn., 65:1 (2024), 164–179
S. V. Pchelintsev, “Construction and applications of an additive basis for the relatively free associative algebra with the lie nilpotency identity of degree 5”, Siberian Math. J., 61:1 (2020), 139–153
A. V. Grishin, “Asymptotics of the Codimensions cn in the Algebra F(7)”, Math. Notes, 104:1 (2018), 22–28
Citation in format AMSBIB
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