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arXiv · 2102.08439

Dilation theory for right LCM semigroup dynamical systems

Marcelo Laca·Boyu Li
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Abstract

This paper examines actions of right LCM semigroups by endomorphisms of C*-algebras that encode an additional structure of the right LCM semigroup. We define contractive covariant representations for these semigroup dynamical systems and prove a generalized Stinespring's dilation theorem showing that these representations can be dilated if and only if the map on the C*-algebra is unital and completely positive. This generalizes earlier results about dilations of right LCM semigroups of contractions. In addition, we also give sufficient conditions under which a contractive covariant representation of a right LCM system can be dilated to an isometric representation of the boundary quotient.

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Marcelo Laca, Boyu Li. 2021-02-16. Dilation theory for right LCM semigroup dynamical systems. https://doi.org/10.1016/j.jmaa.2021.125586

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