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november 2020 Nuclear Group Algebras for Finitely Generated Groups
Michel Cahen, Simone Gutt, Stefan Waldmann
Bull. Belg. Math. Soc. Simon Stevin 27(4): 567-594 (november 2020). DOI: 10.36045/j.bbms.200304

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.

Citation

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Michel Cahen. Simone Gutt. Stefan Waldmann. "Nuclear Group Algebras for Finitely Generated Groups." Bull. Belg. Math. Soc. Simon Stevin 27 (4) 567 - 594, november 2020. https://doi.org/10.36045/j.bbms.200304

Information

Published: november 2020
First available in Project Euclid: 20 November 2020

MathSciNet: MR4177395
Digital Object Identifier: 10.36045/j.bbms.200304

Subjects:
Primary: 20C07, 43A20, 46A11
Secondary: 13J10, 53D55

Rights: Copyright © 2020 The Belgian Mathematical Society

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Vol.27 • No. 4 • november 2020
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