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NON-COCOMMUTATIVE C*-BIALGEBRA DEFINED AS THE DIRECT SUM OF FREE GROUP C*-ALGEBRAS

Part of: Hopf algebras, quantum groups and related topics Topological (rings and) algebras with an involution

Published online by Cambridge University Press:  21 July 2015

KATSUNORI KAWAMURA
KATSUNORI KAWAMURA*
Affiliation:
College of Science and Engineering, Ritsumeikan University, 1-1-1 Noji Higashi, Kusatsu, Shiga 525-8577, Japan e-mail: kawamurakk3@gmail.com
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Abstract

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Leti ${\Bbb F}$n be the free group of rank n and let $\bigoplus C^{*}({\Bbb F}_{n})$ denote the direct sum of full group C*-algebras $C^{*}({\Bbb F}_{n})$ of ${\Bbb F}_{n} (1\leq n<\infty$). We introduce a new comultiplication Δϕ on $\bigoplus C^{*}({\Bbb F}_{n})$ such that $(\bigoplus C^{*}({\Bbb F}_{n}),\,\Delta_{\varphi})$ is a non-cocommutative C*-bialgebra. With respect to Δϕ, the tensor product π⊗ϕπ′ of any two representations π and π′ of free groups is defined. The operation ×ϕ is associative and non-commutative. We compute its tensor product formulas of several representations.

MSC classification

Primary: 46K10: Representations of topological algebras with involution
Secondary: 16T10: Bialgebras
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 58 , Issue 1 , January 2016 , pp. 119 - 136
Copyright
Copyright © Glasgow Mathematical Journal Trust 2015 

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