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, . . . , 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 ≥ 2.

Giambruno, A., MISHCHENKO AND M ZAICEV, S. (2007). Codimension growth of two-dimensional algebras. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 135, 3405-3415.

Codimension growth of two-dimensional algebras

GIAMBRUNO, Antonino;
2007-01-01

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, . . . , 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 ≥ 2.
Giambruno, A., MISHCHENKO AND M ZAICEV, S. (2007). Codimension growth of two-dimensional algebras. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 135, 3405-3415.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10447/13813
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