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On the Connes–Kasparov isomorphism, I: The reduced C*-algebra of a real reductive group and the K-theory of the tempered dual.
- Source :
-
Japanese Journal of Mathematics . Apr2024, Vol. 19 Issue 1, p67-109. 43p. - Publication Year :
- 2024
-
Abstract
- This is the first of two papers dedicated to the detailed determination of the reduced C*-algebra of a connected, linear, real reductive group up to Morita equivalence, and a new and very explicit proof of the Connes–Kasparov conjecture for these groups using representation theory. In this part we shall give details of the C*-algebraic Morita equivalence and then explain how the Connes–Kasparov morphism in operator K-theory may be computed using what we call the Matching Theorem, which is a purely representation-theoretic result. We shall prove our Matching Theorem in the sequel, and indeed go further by giving a simple, direct construction of the components of the tempered dual that have non-trivial K-theory using David Vogan's approach to the classification of the tempered dual. [ABSTRACT FROM AUTHOR]
- Subjects :
- *ISOMORPHISM (Mathematics)
*REPRESENTATIONS of groups (Algebra)
*K-theory
Subjects
Details
- Language :
- English
- ISSN :
- 02892316
- Volume :
- 19
- Issue :
- 1
- Database :
- Academic Search Index
- Journal :
- Japanese Journal of Mathematics
- Publication Type :
- Academic Journal
- Accession number :
- 176033006
- Full Text :
- https://doi.org/10.1007/s11537-024-2220-2