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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Commutative twisted group algebras

Author: Harvey A. Smith
Journal: Trans. Amer. Math. Soc. 197 (1974), 315-326
MSC: Primary 22D15; Secondary 46J20
MathSciNet review: 0364538
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Abstract: A twisted group algebra $ {L^1}(A,G;T,\alpha )$ is commutative iff A and G are, T is trivial and $ \alpha $ is symmetric: $ \alpha (\gamma ,g) = \alpha (g,\gamma )$. The maximal ideal space $ {L^1}(A,G;\alpha )\hat \emptyset $ of a commutative twisted group algebra is a principal $ G\hat \emptyset $ bundle over $ A\hat \emptyset $. A class of principal $ G\hat \emptyset $ bundles over second countable locally compact M is defined which is in 1-1 correspondence with the (isomorphism classes of) $ {C_\infty }(M)$-valued commutative twisted group algebras on G. If G is finite only locally trivial bundles can be such duals, but in general the duals need not be locally trivial.

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Article copyright: © Copyright 1974 American Mathematical Society