When a completion of the universal enveloping algebra is a Banach PI-algebra?
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2022
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| _version_ | 1866910627698573312 |
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| author | Aristov, Oleg |
| author_facet | Aristov, Oleg |
| contents | 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 $\mathfrak{n}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2204_07393 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | When a completion of the universal enveloping algebra is a Banach PI-algebra? Aristov, Oleg Functional Analysis 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 $\mathfrak{n}$. |
| title | When a completion of the universal enveloping algebra is a Banach PI-algebra? |
| topic | Functional Analysis |
| url | https://arxiv.org/abs/2204.07393 |