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The covariance algebra of an extended covariant system

Published online by Cambridge University Press:  24 October 2008

Ronny Rousseau
Ronny Rousseau
Affiliation:
Katholieke Universiteit Leuven, Belgium
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Extract

Let M be a von Neumann algebra acting on a Hilbert space , and let G be a locally compact group. We consider an extension of G by , the unitary group of M. If the triple satisfies an additional axiom, we say that it is an extended covariant system. We define a Hilbert space and operators , acting on . The von Neumann algebra is then the covariance algebra of the extended covariant system , denoted by .

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 85 , Issue 2 , March 1979 , pp. 271 - 280
Copyright
Copyright © Cambridge Philosophical Society 1979

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References

REFERENCES

(1)Dang Ngoc, N.Produits croisés restreints et extensions de groupes Mai 1975 (preprint).Google Scholar
(2)Dixmier, J.Les algèbres d'opérateurs dans l'espace hilbertien (Gauthier-Villars, Paris, 1969).Google Scholar
(3)Douady, A. and Dal Soglio-Hérault, L.Existence de sections pour un fibré de Banach au sens de Fell preprint. See also ((4); appendix).Google Scholar
(4)Fell, J. M. G.Induced representations and Banach *-algebraic bundles Lecture notes in Math. no. 582 (Berlin–Heidelberg–New York, Springer–Verlag, 1977).CrossRefGoogle Scholar
(5)Gaal, S. A.Linear analysis and representation theory (Berlin–Heidelberg–New York, Springer–Verlag, 1973).CrossRefGoogle Scholar
(6)Husemoller, D.Fibre bundles (New York, McGraw-Hill Book Co., 1966).CrossRefGoogle Scholar
(7)Rousseau, R.The left Hilbert algebra associated to a semi-direct product Math. Proc. Cambridge Philos. Soc. 82 (1977), 411–418.CrossRefGoogle Scholar
(8)Sutherland, C.Type analysis of the regular representation of a non-unimodular group, Queen's Math. Preprint (1975).Google Scholar
(9)Sutherland, C.Cohomology and extensions of von Neumann algebras I Queen's Math. Preprint (1975).Google Scholar
(10)Sutherland, C.Cohomology and extensions of von Neumann algebras II Oslo preprint (1976).Google Scholar
(11)Takesaki, M.Duality for crossed products and the structure of von Neumann algebras of type III Acta Math. 131 (1973), 249–308.CrossRefGoogle Scholar
(12)Van Daele, A.Continuous crossed products and type III von Neumann algebras Lecture notes of the London Math. Soc. no. 31 (Cambridge University Press, 1978).CrossRefGoogle Scholar