A note on isomorphisms of groups algebras

Wood, Geoffrey V.

doi:10.1090/S0002-9939-1970-0259503-6

A note on isomorphisms of groups algebras

Author: Geoffrey V. Wood
Journal: Proc. Amer. Math. Soc. 25 (1970), 771-775
MSC: Primary 42.56; Secondary 46.00
DOI: https://doi.org/10.1090/S0002-9939-1970-0259503-6
MathSciNet review: 0259503
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Abstract: In this note, it is shown that, if ${G_1},\;{G_2}$ are compact groups, and $C({G_1}),\;C({G_2})$ are the (convolution) algebras of continuous, complex-valued functions on ${G_1}$ and ${G_2}$ respectively, then the existence of a norm-decreasing algebra-isomorphism of $C({G_1})$ onto $C({G_2})$ ensures that the groups are isomorphic. The corresponding theorem with ${G_1}$ and ${G_2}$ locally finite discrete groups is also proved.

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