On existence of PI-exponents of unital algebras

Abstract

We construct a family of unital non-associative algebras $\{T_{\alpha }|2<\alpha \in \mathbb{R}\}$ such that $\underline{exp}(T_{\alpha })=2$, whereas $\alpha \le \overline{exp}(T_{\alpha })\le \alpha +1$. In particular, it follows that ordinary PI-exponent of codimension growth of algebra $T_{\alpha }$ does not exist for any $\alpha >2$. This is the first example of a unital algebra whose PI-exponent does not exist.

Cited by in corpus (1)

• On existence of PI-exponent of algebras with involution