Department of Mathematics
"Some weighted group algebras are operator algebras"
(University of Saskatchewan, Canada)
Abstract: Let G be a finitely generated group with polynomial growth, and let w be a weight, i.e. a sub-multiplicative function on G with positive values. We study when the weighted group algebra ᶩ ¹ (G, w) is isomorphic to an operator algebra. We show that ᶩ1 (G, w) is isomorphic to an operator algebra if w is a polynomial weight with large enough degree or an exponential weight of order 0 < α < 1. We will demonstrate the order of growth of G plays an important role in this question. Moreover, the algebraic centre of ᶩ1 (G, w) is isomorphic to a Q-algebra and hence satisfies a multi-variable von Neumann inequality. We also present a more detailed study of our results when G is the d-dimensional integers Zd and 3-dimensional discrete Heisenberg group H3 (Z). The case of the free group with two generators will be considered as a counter example of groups with exponential growth.
This is a joint work with Nico Spronk (University of Waterloo, Canada)and Hun Hee Lee (Seoul National University, Canada).
Date: Monday, April, 2016
Place: Mathematics Seminar Room, SA-141
Tea and cookies will be served before the seminar.
All are cordially invited