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

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.

28 pages, to appear in Indiana Univ. Math. J

References in corpus (4)

• The Regular C*-algebra of an Integral Domain
• Equilibrium states on right LCM semigroup C*-algebras
• The boundary quotient for algebraic dynamical systems
• The Cuntz Algebra Q_N and C*-Algebras of Product Systems

Cited by in corpus (11)

• Equilibrium states on right LCM semigroup C*-algebras
• The boundary quotient for algebraic dynamical systems
• Nica-Toeplitz algebras associated with product systems over right LCM semigroups
• The inner structure of boundary quotients of right LCM semigroups
• Representations of the inverse hull of a 0-left cancellative semigroup
• Co-universality and controlled maps on product systems over right LCM-semigroups
• The Nica-Toeplitz algebras of dynamical systems over abelian lattice-ordered groups as full corners
• Graph products and the absence of property (AR)
• Algebraic actions I. C*-algebras and groupoids
• Amenability and functoriality of right-LCM semigroup C*-algebras
• Zappa-Szép actions of groups on product systems