On C*-algebras associated to right LCM semigroups

Abstract

We initiate the study of the internal structure of C*-algebras associated to a left cancellative semigroup in which any two principal right ideals are either disjoint or intersect in another principal right ideal; these are variously called right LCM semigroups or semigroups that satisfy Clifford's condition. Our main findings are results about uniqueness of the full semigroup C*-algebra. We build our analysis upon a rich interaction between the group of units of the semigroup and the family of constructible right ideals. As an application we identify algebraic conditions on S under which C*(S) is purely infinite and simple.

31 pages

References in corpus (5)

• Nuclearity of semigroup C*-algebras and the connection to amenability
• Inverse semigroup C*-algebras associated with left cancellative semigroups
• C*-algebras associated with endomorphisms of groups
• $C^{\ast }$-algebras of inverse semigroups: amenability and weak containment
• Semigroup C*-algebras of $ax+b$-semigroups

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