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The Brauer group of a compact Hausdorff space and $ n$-homogeneous $ C\sp{\ast} $-algebras

Author: Roger Howe
Journal: Proc. Amer. Math. Soc. 34 (1972), 209-214
MSC: Primary 46L05
MathSciNet review: 0305088
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Abstract: The structure of all n-homogeneous $ {C^\ast}$-algebras with a given compact Hausdorff space X as maximal ideal space is looked at from a cohomological standpoint. Such algebras are matrix algebra bundles over X, and by means of fibrewise tensor products, a group, $ B(X)$, analogous to the Brauer group of field theory, is constructed. A partial cohomological description of this group is given. Projective representations of finite groups are used to provide examples where $ B(X)$ is precisely computable and non-trivial.

References [Enhancements On Off] (What's this?)

  • [1] J. Dixmier and A. Douady, Champs continus d'espaces hilbertiens et de $ {C^\ast}$-algèbres, Bull. Soc. Math. France 91 (1963), 227-284. MR 29 #485. MR 0163182 (29:485)
  • [2] J. Dixmier, Les $ {C^\ast}$-algèbres et leurs représentations, Cahiers Scientifiques, fasc. XXIX, Gauthier-Villars, Paris, 1964. MR 30 #1404. MR 0171173 (30:1404)
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Keywords: n-homogeneous $ {C^\ast}$-algebra, Brauer group, compact Hausdorff space
Article copyright: © Copyright 1972 American Mathematical Society

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