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 ¹ (G, w) is isomorphic to an operator algebra. We show that 1 (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 1 (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

Time: 15:40

Place: Mathematics Seminar Room, SA-141



Tea and cookies will be served before the seminar.

All are cordially invited