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COMPACT ELEMENTS AND OPERATORS OF QUANTUM GROUPS

Published online by Cambridge University Press:  10 June 2016

MASSOUD AMINI
Affiliation:
Department of Mathematics, Tarbiat Modares University, P.O.Box 14115-134, Tehran, Iran e-mail: [email protected]
MEHRDAD KALANTAR
Affiliation:
Institute of Mathematics of the Polish Academy of Sciences, ul. Sniadeckich 8, 00–956 Warszawa, Poland
ALIREZA MEDGHALCHI
Affiliation:
Department of Mathematics, Kharazmi University (Tarbiat Moallem University), 50, Taleghani Ave., 15618, Tehran, Iran e-mail: [email protected], [email protected]
AHMAD MOLLAKHALILI
Affiliation:
Department of Mathematics, Kharazmi University (Tarbiat Moallem University), 50, Taleghani Ave., 15618, Tehran, Iran e-mail: [email protected], [email protected]
MATTHIAS NEUFANG
Affiliation:
School of Mathematics and Statistics, Carleton University, Ottawa, Ontario, CanadaK1S 5B6, and Université Lille 1 - Sciences et Technologies, U.F.R. de Mathématiques, Laboratoire de Mathématiques Paul Painlevé - UMR CNRS 8524, 59655 Villeneuve d'Ascq Cédex, France e-mail: [email protected]
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Abstract

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A locally compact group G is compact if and only if its convolution algebras contain non-zero (weakly) completely continuous elements. Dually, G is discrete if its function algebras contain non-zero completely continuous elements. We prove non-commutative versions of these results in the case of locally compact quantum groups.

Type
Research Article
Copyright
Copyright © Glasgow Mathematical Journal Trust 2016 

References

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