English

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.

Keywords

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

R2 v1 2026-06-22T16:30:33.640Z