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 UT2(Wλ) or End(Wμ) for some integral dominant weight λ, μ with μ ≠ 0. In the special case L = sl2 we prove that this is a sufficient condition too.
Lie semisimple algebras of derivations and varieties of PI-algebras with almost polynomial growth
Argenti S.
2024-01-01
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 UT2(Wλ) or End(Wμ) for some integral dominant weight λ, μ with μ ≠ 0. In the special case L = sl2 we prove that this is a sufficient condition too.File in questo prodotto:
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Lie semisimple algebras of derivations and varieties of Pi-algebras with almost polynomial growth.pdf
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