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Full-Text Articles in Social and Behavioral Sciences
Cartan Subalgebras In C*-Algebras Of Hausdorff Étale Groupoids, Jonathan H. Brown, Gabriel Nagy, Sarah Reznikoff, Aidan Sims, Dana P. Williams
Cartan Subalgebras In C*-Algebras Of Hausdorff Étale Groupoids, Jonathan H. Brown, Gabriel Nagy, Sarah Reznikoff, Aidan Sims, Dana P. Williams
Faculty of Engineering and Information Sciences - Papers: Part A
The reduced C*-algebra of the interior of the isotropy in any Hausdorff étale groupoid G embeds as a C*-subalgebra M of the reduced C*-algebra of G. We prove that the set of pure states of M with unique extension is dense, and deduce that any representation of the reduced C*-algebra of G that is injective on M is faithful. We prove that there is a conditional expectation from the reduced C*-algebra of G onto M if and only if the interior of the isotropy in G is closed. Using this, we prove that when the interior of the isotropy is …
Af-Embeddability Of 2-Graph Algebras And Quasidiagonality Of K-Graph Algebras, Lisa Orloff Clark, Astrid An Huef, Aidan Sims
Af-Embeddability Of 2-Graph Algebras And Quasidiagonality Of K-Graph Algebras, Lisa Orloff Clark, Astrid An Huef, Aidan Sims
Faculty of Engineering and Information Sciences - Papers: Part A
We characterise quasidiagonality of the C*-algebra of a cofinal k-graph in terms of an algebraic condition involving the coordinate matrices of the graph. This result covers all simple k-graph C*-algebras. In the special case of cofinal 2-graphs we further prove that AF-embeddability, quasidiagonality and stable finiteness of the 2-graph algebra are all equivalent.