Dilations of interaction groups that extend actions of Ore semigroups

Details Dilations of interaction groups that extend actions of Ore semigroups Dilations of interaction groups that extend actions of Ore semigroups

2010-08-05

arxiv.org/abs/1008.0903v1

Mathematics

Operator Algebras

17 pages

Scientific paper

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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