A Mackey embedding for reduced C*-algebras of real reductive groups
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866917301032321024 |
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| author | Clare, Pierre Higson, Nigel Román, Angel |
| author_facet | Clare, Pierre Higson, Nigel Román, Angel |
| contents | The purpose of this paper is construct an embedding of the C*-algebra of the Cartan motion group of a real reductive group G into the reduced C*-algebra of G itself. The embedding has a number of applications: we shall use it to characterize the Mackey bijection from the tempered dual of G into the unitary dual of the motion group; to characterize the continuous field of reduced group C*-algebras arising from the contraction of G to its Cartan motion group; and to characterize the Connes-Kasparov assembly map in operator K-theory. Our results continue and complete a project that was begun several years ago by the last two authors, who considered the case of complex groups. In the real case, detailed information from the theory of R-groups is used in the construction. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_02504 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Mackey embedding for reduced C*-algebras of real reductive groups Clare, Pierre Higson, Nigel Román, Angel Representation Theory K-Theory and Homology Operator Algebras 22D25 (primary), 22E45, 46L80 The purpose of this paper is construct an embedding of the C*-algebra of the Cartan motion group of a real reductive group G into the reduced C*-algebra of G itself. The embedding has a number of applications: we shall use it to characterize the Mackey bijection from the tempered dual of G into the unitary dual of the motion group; to characterize the continuous field of reduced group C*-algebras arising from the contraction of G to its Cartan motion group; and to characterize the Connes-Kasparov assembly map in operator K-theory. Our results continue and complete a project that was begun several years ago by the last two authors, who considered the case of complex groups. In the real case, detailed information from the theory of R-groups is used in the construction. |
| title | A Mackey embedding for reduced C*-algebras of real reductive groups |
| topic | Representation Theory K-Theory and Homology Operator Algebras 22D25 (primary), 22E45, 46L80 |
| url | https://arxiv.org/abs/2508.02504 |