Lie semisimple algebras of derivations and varieties of PI-algebras with almost polynomial growth

Argenti, Sebastiano

doi:10.1090/proc/16896

Lie semisimple algebras of derivations and varieties of PI-algebras with almost polynomial growth
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by Sebastiano Argenti;

Proc. Amer. Math. Soc. 152 (2024), 4217-4229

DOI: https://doi.org/10.1090/proc/16896

Published electronically: July 31, 2024

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Abstract:

We consider associative algebras with an action by derivations by some finite dimensional and semisimple Lie algebra. We prove that if a differential variety has almost polynomial growth, then it is generated by one of the algebras $UT_2(W_\lambda )$ or $End(W_\mu )$ for some integral dominant weight $\lambda ,\mu$ with $\mu \neq 0$. In the special case $L=\mathfrak {sl}_2$ we prove that this is a sufficient condition too.

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