Friday, October 16, 2015 — 3:30 PM EDT

Jason Crann, Department of Pure Math, University of Waterloo

“Homological manifestations of quantum group amenability”

We present a non-relative homological characterization of quantum group amenability in terms of 1-injectivity of the dual L(Gˆ) as an operator module over its predual L1(Gˆ). This result not only establishes the equivalence between amenability of a locally compact group G and 1-injectivity of its group von Neumann algebra L(G) as an A(G)-module, it provides a novel tool for the development of abstract harmonic analysis on locally compact quantum groups. Indeed, we present several applications, including a proof that closed quantum subgroups (in the sense of Vaes) of amenable quantum groups are amenable; a decomposability result for completely bounded L1(Gˆ)-module maps on L(Gˆ), and a simplified proof that amenable discrete quantum groups have co-amenable compact duals which avoids the use of modular theory. Time permitting, we will also discuss recent work on relative biflatness of the Fourier algebra.

MC 5417

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