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arXiv · 2006.10335

On existence of PI-exponents of unital algebras

Dušan D. Repovš·Mikhail V. Zaicev
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Abstract

We construct a family of unital non-associative algebras $\{T_\alpha\vert~ 2<\alpha\in\mathbb R\}$ 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.

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Dušan D. Repovš, Mikhail V. Zaicev. 2020-06-18. On existence of PI-exponents of unital algebras. https://doi.org/10.3934/era.2020044

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