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arXiv · 1503.01599

C*-Algebras of algebraic dynamical systems and right LCM semigroups

Nathan Brownlowe·Nadia S. Larsen·Nicolai Stammeier
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Abstract

We introduce algebraic dynamical systems, which consist of an action of a right LCM semigroup by injective endomorphisms of a group. To each algebraic dynamical system we associate a C*-algebra and describe it as a semigroup C*-algebra. As part of our analysis of these C*-algebras we prove results for right LCM semigroups. More precisely we discuss functoriality of the full semigroup C*-algebra and compute its K-theory for a large class of semigroups. We introduce the notion of a Nica-Toeplitz algebra of a product system over a right LCM semigroup, and show that it provides a useful alternative to study algebraic dynamical systems.

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Nathan Brownlowe, Nadia S. Larsen, Nicolai Stammeier. 2017-06-19. C*-Algebras of algebraic dynamical systems and right LCM semigroups. https://doi.org/10.1512/iumj.2018.67.7527

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