On existence of PI-exponent of algebras with involution

DOI10.1016/J.JALGEBRA.2022.09.013arXiv2210.10589MaRDI QIDQ6414454

Dušan Repovš, Mikhail Zaicev

Publication date: 19 October 2022

Abstract: We study polynomial identities of algebras with involution of nonassociative algebras over a field of characteristic zero. We prove that the growth of the sequence of $*$-codimensions of a finite-dimensional algebra is exponentially bounded. We construct a series of finite-dimensional algebras with fractional $*$-PI-exponent. We also construct a family of infinite-dimensional algebras $C_{a}lpha$ such that ${mexp}^{*}(C_{a}lpha)$ does not exist.

Mathematics Subject Classification ID

Growth rate, Gelfand-Kirillov dimension (16P90) (T)-ideals, identities, varieties of associative rings and algebras (16R10)

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