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

Brownlowe, Nathan; Larsen, Nadia S.; Stammeier, Nicolai
Journal article; SubmittedVersion
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BLS-submission.pdf (510.8Kb)
Year
2018
Permanent link
http://urn.nb.no/URN:NBN:no-60548

CRIStin
1490614

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Appears in the following Collection
  • Matematisk institutt [2450]
  • CRIStin høstingsarkiv [15888]
Original version
Indiana University Mathematics Journal. 2018
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.

This is a submitted version of this article, and has not yet been published. The final version will be published in the © Indiana University Mathematics Journal.
 
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