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arXiv · 2204.07393

When a completion of the universal enveloping algebra is a Banach PI-algebra?

Oleg Aristov
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Abstract

We prove that a Banach algebra $B$ that is a completion of the universal enveloping algebra of a finite-dimensional complex Lie algebra $\mathfrak{g}$ satisfies a polynomial identity if and only if the nilpotent radical $\mathfrak{n}$ of $\mathfrak{g}$ is associatively nilpotent in $B$. Furthermore, this holds if and only if a certain polynomial growth condition is satisfied on $\mathfrak{n}$.

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Oleg Aristov. 2022-04-15. When a completion of the universal enveloping algebra is a Banach PI-algebra?. https://doi.org/10.1017/s0004972722000788

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