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- Title
WHEN IS A COMPLETION OF THE UNIVERSAL ENVELOPING ALGEBRA A BANACH PI-ALGEBRA?
- Authors
ARISTOV, O. YU.
- 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 $\mathfrak {n}$.
- Subjects
UNIVERSAL algebra; BANACH algebras; NILPOTENT Lie groups; LIE algebras; BANACH spaces; POLYNOMIALS
- Publication
Bulletin of the Australian Mathematical Society, 2023, Vol 107, Issue 3, p493
- ISSN
0004-9727
- Publication type
Article
- DOI
10.1017/S0004972722000788