Codimension growth of two-dimensional non-associative algebras

Giambruno, A.; Mishchenko, S.; Zaicev, M.

doi:10.1090/S0002-9939-07-08673-X

Codimension growth of two-dimensional non-associative algebras
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by A. Giambruno, S. Mishchenko and M. Zaicev PDF

Proc. Amer. Math. Soc. 135 (2007), 3405-3415 Request permission

Abstract:

Let $F$ be a field of characteristic zero and let $A$ be a two- dimensional non-associative algebra over $F$. We prove that the sequence $c_n(A), n\!=\!1,2,\ldots ,$ of codimensions of $A$ is either bounded by $n+1$ or grows exponentially as $2^n$. We also construct a family of two-dimensional algebras indexed by rational numbers with distinct T-ideals of polynomial identities and whose codimension sequence is $n+1$, $n\ge 2$.

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