Notes on C*-algebras, representations, and Morita equivalence (with a view toward C*-algebras of reductive groups)
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866912917305163776 |
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| author | Crisp, Tyrone |
| author_facet | Crisp, Tyrone |
| contents | These notes give an expanded account of my lectures at the CIRM-IHP research school on 'Methods in representation theory and operator algebras', January 6-10, 2025. Their main goal is to explain a proof of a theorem of A. Wassermann, that identifies the reduced C*-algebra of a real reductive group, up to Morita equivalence, with a direct sum of much simpler C*-algebras. Along the way we introduce the basic theory of representations and Morita equivalence of C*-algebras that is needed to understand the theorem and its proof. The target audience is Masters- and PhD-level students, and other mathematicians who are not specialists in operator algebras. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2602_18601 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Notes on C*-algebras, representations, and Morita equivalence (with a view toward C*-algebras of reductive groups) Crisp, Tyrone Operator Algebras Representation Theory 22D25 (Primary) 46L05, 22E46 These notes give an expanded account of my lectures at the CIRM-IHP research school on 'Methods in representation theory and operator algebras', January 6-10, 2025. Their main goal is to explain a proof of a theorem of A. Wassermann, that identifies the reduced C*-algebra of a real reductive group, up to Morita equivalence, with a direct sum of much simpler C*-algebras. Along the way we introduce the basic theory of representations and Morita equivalence of C*-algebras that is needed to understand the theorem and its proof. The target audience is Masters- and PhD-level students, and other mathematicians who are not specialists in operator algebras. |
| title | Notes on C*-algebras, representations, and Morita equivalence (with a view toward C*-algebras of reductive groups) |
| topic | Operator Algebras Representation Theory 22D25 (Primary) 46L05, 22E46 |
| url | https://arxiv.org/abs/2602.18601 |