Commutative twisted group algebras
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- by Harvey A. Smith
- Trans. Amer. Math. Soc. 197 (1974), 315-326
- DOI: https://doi.org/10.1090/S0002-9947-1974-0364538-7
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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.References
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Bibliographic Information
- © Copyright 1974 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 197 (1974), 315-326
- MSC: Primary 22D15; Secondary 46J20
- DOI: https://doi.org/10.1090/S0002-9947-1974-0364538-7
- MathSciNet review: 0364538