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

Pub Date : 2024-05-01 DOI:10.1090/proc/16896

Sebastiano Argenti

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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 U T 2 ( W λ ) UT_2(W_\lambda ) or E n d ( W μ ) End(W_\mu ) for some integral dominant weight λ , μ \lambda ,\mu with μ ≠ 0 \mu \neq 0 . In the special case L = s l 2 L=\mathfrak {sl}_2 we prove that this is a sufficient condition too.

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具有几乎多项式增长的导数的列半简单代数和 PI 代数品种

我们考虑的是具有某种有限维半简单李代数派生作用的关联代数。我们证明，如果一个微分方程具有几乎多项式的增长，那么它是由 U T 2 ( W λ ) UT_2(W_\lambda)或 E n d ( W μ ) End(W_\mu ) 中的一个代数生成的，对于某个积分主重 λ , μ \lambda ,\mu μ ≠ 0 \mu \neq 0。在 L = s l 2 L=\mathfrak {sl}_2 的特殊情况下，我们证明这也是一个充分条件。

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