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On the normal version of the simplicial cohomology of operator algebras

Published online by Cambridge University Press:  17 April 2009

A.Ya. Helemskii  and
Z.A. Lykova
A.Ya. Helemskii
Affiliation:
Chair of function Theory and Functional Analysis Faculty of Mechanics and Mathematics, Moscow State University, Moscow 119899GSP, Russia
Z.A. Lykova
Affiliation:
Chair of Algebra and Analysis, Moscow Institute of Electronic Machine, Industry B.Vuzovskii 3/12 Moscow 109028, Russia
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We show that the normal version (R, R.) of the Banach simplicial cohomology of operator algebras can be expressed in terms of the functor Ext on the category of Banach R-bimodules. As an application, we prove that (R, R*) = Hn(R, R*) and thus the latter space vanishes for some von Heumann algebras for positive τ.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 48 , Issue 3 , December 1993 , pp. 407 - 410
Copyright
Copyright © Australian Mathematical Society 1993

References

[1]Christensen, E. and Sinclair, A.M., ‘On the vanishing of H n(A, A*) for certain C*-algebras’, Pacific J. Math. 137 (1989), 55–63.Google Scholar
[2]Haagerup, U., ‘All nuclear C*-algebras are amenable’, Invent. Math. 73 (1983), 305–319.CrossRefGoogle Scholar
[3]Helemskii, A.Ya., ‘The homological essence of Connes amenability: injectivity of the predual bimodule’, (in Russian), Mat. Sb. 180 (1989), 1680–1690. Math. USSR Sbornik 68 (1991), 555–566.Google Scholar
[4]Helemskii, A.Ya., The Homology in Banach and topological algebras, (in Russian) (Moscow Univ. Press, Moscow, 1986). (Kluwer Academic Publishers, Dordrecht, 1989) (in English).CrossRefGoogle Scholar
[5]Helemskii, A.Ya., ‘Expression of the normal cohomology in terms of “Ext”, and some applications’, Math. Nachr. 145 (1990), 55–58.CrossRefGoogle Scholar
[6]Johnson, B.E., Kadison, R.V. and Ringrose, J.R., ‘Cohomology of operator algebras, III’, Bull. Soc. Math. France 100 (1972), 73–96.CrossRefGoogle Scholar