A Homological Property and Arens Regularity of Locally Compact Quantum Groups

Canadian mathematical bulletin

Rasoul Nasr-Isfahani¹  Mehdi Nemati¹  Mohammad Reza Ghanei² 

[1] School of Mathematics, Institute for Research in Fundamental Sciences (IPM), P.O. Box: 19395--5746, Tehran, Iran;Department of Mathematics, Khansar Faculty of Mathematics and Computer Science, Khansar, Iran

关键词: amenability;    Arens regularity;    co-amenability;    locally compact quantum group;    homological property;   

DOI  :  10.4153/CMB-2016-052-x

学科分类：数学（综合）

来源: University of Toronto Press * Journals Division

【 摘 要 】

We characterize two important notions of amenability and compactnessof a locally compact quantum group ${mathbb G}$ in terms of certainhomological 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 resultby Hu, Neufang and Ruan.

【 授权许可】

Unknown