Boundary quotients of C*-algebras of right LCM semigroups
By Charles Starling. 2014
49 citations recorded by the source corpus.
We study C*-algebras associated to right LCM semigroups, that is, semigroups which are left cancellative and for which any two principal right ideals are either disjoint or intersect in another principal right ideal. If $P$ is such a semigroup, its C*-algebra admits a natural boundary quotient $\mathcal{Q}(P)$. We show that $\mathcal{Q}(P)$ is isomorphic to the tight C*-algebra of a certain inverse semigroup associated to $P$, and thus is isomorphic to the C*-algebra of an \'etale groupoid. We use this to give conditions on $P$ which guarantee that $\mathcal{Q}(P)$ is simple and purely infinite, and give applications to self-similar groups and Zappa-Sz\'ep products of semigroups.
Subfields: Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/35f4cb8424538d66669dacace4d2f3c12a9c19fa
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In Geometry and Topology
In Mathematical Physics
- Enrique Pardo
- R. Exel
- Ben Steinberg
- Mark V. Lawson
- Charles Starling
- Aidan Sims
- L. O. Clark
- Mikhailo Dokuchaev
Citations in the corpus
- Self-similar graphs, a unified treatment of Katsura and Nekrashevych C*-algebras (2014, background): “nd self-similar graphs 5 Some of the results in the present paper appeared in the preprints [10] and [11], which in turn are to be replaced by the present work. We would also like to mention [13] and [32], which are strongly related to the algebras we study here. In [13] conditions are given for OG,”
- The tight groupoid of an inverse semigroup (2014, background): “[3,4,7,22]) begs for a unified treatment of questions of relevance in the study of the structure of such C*-algebras.”