Nuclear Group Algebras for Finitely Generated Groups
Group Theory
2016-10-26 v1
Abstract
We study completions of the group algebra of a finitely generated group and relate nuclearity of such a completion to growth properties of the group. This extends previous work of Jolissaint on nuclearity of rapidly decreasing functions on a finitely generated group to more general weights than polynomial decrease. The new group algebras and their duals are studied in detail and compared to other approaches. As application we discuss the convergence of the complete growth function introduced by Grigorchuk and Nagnibeda.
Cite
@article{arxiv.1610.07746,
title = {Nuclear Group Algebras for Finitely Generated Groups},
author = {Michel Cahen and Simone Gutt and Stefan Waldmann},
journal= {arXiv preprint arXiv:1610.07746},
year = {2016}
}
Comments
24 pages