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arXiv · 2210.10589

On existence of PI-exponent of algebras with involution

Dušan D. Repovš·Mikhail V. Zaicev
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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 $C_\alpha$ such that ${\rm exp}^*(C_\alpha)$ does not exist.

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Dušan D. Repovš, Mikhail V. Zaicev. 2022-10-19. On existence of PI-exponent of algebras with involution. https://doi.org/10.1016/j.jalgebra.2022.09.013

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