Toeplitz algebras and the Heisenberg group
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866910761618505728 |
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| author | Cren, Clément |
| author_facet | Cren, Clément |
| contents | We show an isomorphism between an algebra which is naturally constructed from the Toeplitz algebra generated by d-shifts, and an ideal of the C * -algebra of the (2d + 1)-dimensional Heisenberg group. This is a particular case of a more general result for graded nilpotent Lie groups involving symbols in the filtered calculus. The proof presented here however only involves basic functional analysis while still showcasing the ideas of the proof in the general setting. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_18266 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Toeplitz algebras and the Heisenberg group Cren, Clément Differential Geometry Functional Analysis Operator Algebras We show an isomorphism between an algebra which is naturally constructed from the Toeplitz algebra generated by d-shifts, and an ideal of the C * -algebra of the (2d + 1)-dimensional Heisenberg group. This is a particular case of a more general result for graded nilpotent Lie groups involving symbols in the filtered calculus. The proof presented here however only involves basic functional analysis while still showcasing the ideas of the proof in the general setting. |
| title | Toeplitz algebras and the Heisenberg group |
| topic | Differential Geometry Functional Analysis Operator Algebras |
| url | https://arxiv.org/abs/2412.18266 |