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New Deformations of Convolution Algebras and Fourier Algebras on Locally Compact Groups

Published online by Cambridge University Press:  20 November 2018

Hun Hee Lee  and
Sang-gyun Youn
Hun Hee Lee
Affiliation:
Department of Mathematical Sciences and Research Institute of Mathematics, Seoul National University, San56-1 Shinrim-dong Kwanak-gu, Seoul 151-747, Republic of Korea e-mail: hunheelee@snu.ac.kr, yun87654@snu.ac.kr
Sang-gyun Youn
Affiliation:
Department of Mathematical Sciences and Research Institute of Mathematics, Seoul National University, San56-1 Shinrim-dong Kwanak-gu, Seoul 151-747, Republic of Korea e-mail: hunheelee@snu.ac.kr, yun87654@snu.ac.kr
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Abstract

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In this paper we introduce a new way of deforming convolution algebras and Fourier algebras on locally compact groups. We demonstrate that this new deformation allows us to reveal some information about the underlying groups by examining Banach algebra properties of deformed algebras. More precisely, we focus on representability as an operator algebra of deformed convolution algebras on compact connected Lie groups with connection to the real dimension of the underlying group. Similarly, we investigate complete representability as an operator algebra of deformed Fourier algebras on some finitely generated discrete groups with connection to the growth rate of the group.

Keywords

43A2043A3047L3047L25Fourier algebraconvolution algebraoperator algebraBeurling algebra
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 69 , Issue 2 , 01 April 2017 , pp. 434 - 452
Copyright
Copyright © Canadian Mathematical Society 2017

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