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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

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
DOI: https://doi.org/10.1090/S0002-9939-1972-0305088-7
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.


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DOI: https://doi.org/10.1090/S0002-9939-1972-0305088-7
Keywords: n-homogeneous $ {C^\ast}$-algebra, Brauer group, compact Hausdorff space
Article copyright: © Copyright 1972 American Mathematical Society