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Lorentz groups: K-theory of unitary representations and crossed products. (English. Russian original) Zbl 0584.22004
Sov. Math., Dokl. 29, 256-260 (1984); translation from Dokl. Akad. Nauk SSSR 275, 541-545 (1984).
The author describes the ring R(G) of representations and the K-functor \(K^*(C^*(G))\) for the Lorentz groups \(SO_ 0(n,1)\), Spin(n,1) and for their discrete subgroups as well as the K-functor of certain crossed products of these groups with separable \(C^*\)-algebras.
Reviewer: S.Prishchepionok

MSC:
22D25 \(C^*\)-algebras and \(W^*\)-algebras in relation to group representations
22E43 Structure and representation of the Lorentz group
16E20 Grothendieck groups, \(K\)-theory, etc.
18F25 Algebraic \(K\)-theory and \(L\)-theory (category-theoretic aspects)
46L05 General theory of \(C^*\)-algebras
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