Noncommutative Geometry Seminar

Date: October 28, 2020

Time: 1:00PM - 2:00PM

Location: Zoom 942810031

Speaker: Matthew Lorentz, University of Hawai‘i at Mānoa

Title: The Hochschild cohomology of uniform Roe algebras

Abstract: Recently Rufus Willett and I showed that all bounded derivations on Uniform Roe Algebras associated to a bounded geometry metric space X are inner in our paper “Bounded Derivations on Uniform Roe Algebras”. This is equivalent to the first Hochschild cohomology group $H^1(C^*_u(X), C^*_u(X))$ vanishing. It is then natural to ask if all the higher groups $H^n(C^*_u(X), C^*_u(X))$ vanish. To investigate the continuous cohomology of a Uniform Roe Algebra we employ the technique of “reduction of cocycles” where we modify a given cocycle by a coboundary to obtain certain properties. I will discuss this procedure and give examples of calculating the higher cohomology groups.

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