Title

On C*-algebras associated to right LCM semigroups

RIS ID

110325

Publication Details

Brownlowe, N., Larsen, N. S. & Stammeier, N. (2017). On C*-algebras associated to right LCM semigroups. Transactions of the American Mathematical Society, 369 (1), 31-68.

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.

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Link to publisher version (DOI)

http://dx.doi.org/10.1090/tran/6638