Spherical representations of $C^*$-flows I
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2020
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| _version_ | 1866914694880559104 |
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| author | Ueda, Yoshimichi |
| author_facet | Ueda, Yoshimichi |
| contents | We propose an abstract framework of a kind of representation theory for $C^*$-flows, i.e., $C^*$-algebras equipped with one-parameter automorphism groups, as a proper generalization of Olshanski's formalism of unitary representation theory for infinite-dimensional groups such as the infinite-dimensional unitary group $\mathrm{U}(\infty)$. The present framework, in particular, clarifies some overlaps and/or similarities between a certain unitary representation theory of infinite-dimensional groups and existing works in operator algebras, and captures arbitrary projective chains arising from links. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2010_15324 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Spherical representations of $C^*$-flows I Ueda, Yoshimichi Operator Algebras Representation Theory We propose an abstract framework of a kind of representation theory for $C^*$-flows, i.e., $C^*$-algebras equipped with one-parameter automorphism groups, as a proper generalization of Olshanski's formalism of unitary representation theory for infinite-dimensional groups such as the infinite-dimensional unitary group $\mathrm{U}(\infty)$. The present framework, in particular, clarifies some overlaps and/or similarities between a certain unitary representation theory of infinite-dimensional groups and existing works in operator algebras, and captures arbitrary projective chains arising from links. |
| title | Spherical representations of $C^*$-flows I |
| topic | Operator Algebras Representation Theory |
| url | https://arxiv.org/abs/2010.15324 |