On C*-algebras associated to right LCM semigroups

By Nathan Brownlowe, Nadia S. Larsen, Nicolai Stammeier. 2014

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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.

Subfields: Algebra and Number Theory, Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/d2865e21936f96b732a4b693aec8cb0047d397e3