Dilations of semigroup crossed products as crossed products of dilations

Details Dilations of semigroup crossed products as crossed products of dilations Dilations of semigroup crossed products as crossed products of dilations

2010-09-29

arxiv.org/abs/1009.5842v1

Mathematics

Operator Algebras

Scientific paper

Laca constructed a minimal automorphic dilation for every semigroup dynamical system arising from an action of an Ore semigroup by injective endomorphisms of a unital $C^*$-algebra. Here we show that the semigroup crossed product with its action by inner endomorphisms given by the implementing isometries has as minimal automorphic dilation the group crossed product of the original dilation. Applications include recent examples studied by Cuntz and the second named author.

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