We construct a continuous family of algebras over a field of characteristic zero with slow codimension growth bounded by a polynomial of degree 4. This is achieved by building, for any real number α ∈(0, 1) a commutative nonassociative algebra A_α whose codimension sequence c_n(A_α), n =1, 2, ..., is polynomially bounded . As an application we are able to construct a new example of a variety with an infinite basis of identities.
Giambruno, A., Mishchenko, S., Valenti, A., Zaicev M. (2017). Polynomial codimension growth and the Specht problem. JOURNAL OF ALGEBRA, 469, 421-436 [10.1016/j.jalgebra.2016.09.008].
Polynomial codimension growth and the Specht problem
GIAMBRUNO, Antonino;VALENTI, Angela;
2017-01-01
Abstract
We construct a continuous family of algebras over a field of characteristic zero with slow codimension growth bounded by a polynomial of degree 4. This is achieved by building, for any real number α ∈(0, 1) a commutative nonassociative algebra A_α whose codimension sequence c_n(A_α), n =1, 2, ..., is polynomially bounded . As an application we are able to construct a new example of a variety with an infinite basis of identities.
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