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arXiv · 1008.0903

Dilations of interaction groups that extend actions of Ore semigroups

Fernando Abadie
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Abstract

We show that every interaction group extending an action of an Ore semigroup by injective unital endomorphisms of a C*-algebra, admits a dilation to an action of the corresponding enveloping group on another unital C*-algebra, of which the former is a C*-subalgebra: the interaction group is obtained by composing the action with a conditional expectation. The dilation is essentially unique if a certain natural condition of minimality is imposed. If the action is induced by covering maps on the spectrum, then the expectation is faithful.

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Fernando Abadie. 2010-08-05. Dilations of interaction groups that extend actions of Ore semigroups. https://arxiv.org/abs/1008.0903

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