Abstract
We prove that a Banach algebra B that is a completion of the universal enveloping algebra of a finite-dimensional complex Lie algebra satisfies a polynomial identity if and only if the nilpotent radical of is associatively nilpotent in B. Furthermore, this holds if and only if a certain polynomial growth condition is satisfied on.
| Original language | English |
|---|---|
| Pages (from-to) | 493-501 |
| Number of pages | 9 |
| Journal | Bulletin of the Australian Mathematical Society |
| Volume | 107 |
| Issue number | 3 |
| DOIs | |
| State | Published - 5 Jun 2023 |
Keywords
- Banach PI-algebra
- Banach space representation
- nilpotent radical
- polynomial growth
- universal enveloping algebra
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