Cartan subalgebras of non-principal twisted groupoid C*-algebras

Document Type

Presentation Abstract

Presentation Date

3-29-2021

Abstract

An algebraic structure called a C∗-algebra can be built from a group or groupoid (a generalization of a group). In this talk we focus on a special subalgebra, called a Cartan subalgebra, of a particular type of groupoid C∗-algebra whose multiplication is twisted by a circle-valued 2-cocycle. We identify sufficient conditions on a subgroupoid S⊂G so that the twisted C∗-algebra generated by S is a Cartan subalgebra of the twisted C∗-algebra generated by G. We then describe (in terms of G and S) the so-called Weyl groupoid and twist that J. Renault defined in 2008, which give us a different groupoid model for our Cartan pair. Time permitting, we discuss ongoing efforts to apply these results to C∗-algebras of higher rank graphs. This is joint work with A. Duwenig, E. Gillaspy, S. Reznikoff, and S. Wright.

Additional Details

March 29, 2021 at 3:00 p.m. via Zoom

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