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A Homological Property and Arens Regularity of Locally Compact Quantum Groups

  Published:2016-10-04
 Printed: Mar 2017
  • Mohammad Reza Ghanei,
    Department of Mathematics, Khansar Faculty of Mathematics and Computer Science, Khansar, Iran
  • Rasoul Nasr-Isfahani,
    School of Mathematics, Institute for Research in Fundamental Sciences (IPM), P.O. Box: 19395--5746, Tehran, Iran
  • Mehdi Nemati,
    School of Mathematics, Institute for Research in Fundamental Sciences (IPM), P.O. Box: 19395--5746, Tehran, Iran
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Abstract

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 $L^1({\mathbb G})$; in particular, we improve an interesting result by Hu, Neufang and Ruan.
Keywords: amenability, Arens regularity, co-amenability, locally compact quantum group, homological property amenability, Arens regularity, co-amenability, locally compact quantum group, homological property
MSC Classifications: 46L89, 43A07, 46H20, 46M10, 58B32 show english descriptions Other ``noncommutative'' mathematics based on $C^*$-algebra theory [See also 58B32, 58B34, 58J22]
Means on groups, semigroups, etc.; amenable groups
Structure, classification of topological algebras
Projective and injective objects [See also 46A22]
Geometry of quantum groups
46L89 - Other ``noncommutative'' mathematics based on $C^*$-algebra theory [See also 58B32, 58B34, 58J22]
43A07 - Means on groups, semigroups, etc.; amenable groups
46H20 - Structure, classification of topological algebras
46M10 - Projective and injective objects [See also 46A22]
58B32 - Geometry of quantum groups
 

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