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A Homological Property and Arens Regularity of Locally Compact Quantum Groups

Published online by Cambridge University Press:  20 November 2018

Mohammad Reza Ghanei ,
Rasoul Nasr-Isfahani  and
Mehdi Nemati
Mohammad Reza Ghanei
Affiliation:
Department of Mathematics, Khansar Faculty of Mathematics and Computer Science, Khansar, Iran e-mail: mr.ghanei@math.iut.ac.ir
Rasoul Nasr-Isfahani
Affiliation:
School of Mathematics, Institute for Research in Fundamental Sciences (IPM), P.O. Box: 19395–5746, Iran Department of Mathematical Sciences, Isfahan University of Technology, Isfahan 84156-83111, Iran e-mail: isfahani@cc.iut.ac.ir e-mail: m.nemati@cc.iut.ac.ir
Mehdi Nemati
Affiliation:
School of Mathematics, Institute for Research in Fundamental Sciences (IPM), P.O. Box: 19395–5746, Iran Department of Mathematical Sciences, Isfahan University of Technology, Isfahan 84156-83111, Iran e-mail: isfahani@cc.iut.ac.ir e-mail: m.nemati@cc.iut.ac.ir
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Abstract

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We characterize two important notions of amenability and compactness of a locally compact quantum group $\mathbb{G}$ in terms of certain homological properties. For this, we show that $\mathbb{G}$ is character amenable if and only if it is both amenable and co-amenable. We finally apply our results to Arens regularity problems of the quantum group algebra ${{L}^{1}}\left( \mathbb{G} \right)$. In particular, we improve an interesting result by Hu, Neufang, and Ruan.

Keywords

46L8943A0746H2046M1058B32amenabilityArens regularityco-amenabilitylocally compact quantum grouphomological property
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 60 , Issue 1 , 01 March 2017 , pp. 122 - 130
Copyright
Copyright © Canadian Mathematical Society 2017

References

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