Inverse semigroups associated to subshifts

2015/05/07 by Starling, Charles
#20M18 #46L05 #46L55 #Category Theory (math.CT) #Dynamical Systems (math.DS) #FOS: Mathematics #Operator Algebras (math.OA)

paper · doi:10.48550/arxiv.1505.01766

Abstract

The dynamics of a one-sided subshift X can be modeled by a set of partially defined bijections. From this data we define an inverse semigroup S_X and show that it has many interesting properties. We prove that the Carlsen-Matsumoto C*-algebra O_X associated to X is canonically isomorphic to Exel's tight C*-algebra of S_X. As one consequence, we obtain that O_X can be written as a partial crossed product of a commutative C*-algebra by a countable group.

Related

• Subshift semigroups
• Inverse semigroup C*-algebras associated with left cancellative semigroups
• A new uniqueness theorem for the tight C*-algebra of an inverse semigroup
• Inverse Semigroups and Combinatorial C*-Algebras
• C*-crossed products by partial actions and actions of inverse semigroups