Quantum Symmetry Seminar - Patrick DeBonis

Patrick DeBonis
Purdue University

Title
The W* and C*-algebras of Similarity Structure Groups

Abstract
Countable Similarity Structure (CSS) groups are groups of homeomorphisms that can be understood as generalizations of the Thompson groups. We identify a subclass referred to as CSS$^*$ groups that contains the Higman-Thompson groups $V_{d,r}$, the countable R\"over-Nekrashevych groups $V_d(G)$, and the topological full groups of subshifts of finite type of Matui. I will highlight several new properties of both the group von Neumann algebra and reduced group C$^*$-algebra of CSS$^*$ groups. These include primeness of many CSS* group von Neumann algebras and C$^*$-simplicity in certain cases. This is joint work with Eli Bashwinger.

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