Geodesic
A Homological Property and Arens Regularity of Locally Compact Quantum Groups
Canadian mathematical bulletin, Tome 60 (2017) no. 1, pp. 122-130

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DOI

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.
DOI : 10.4153/CMB-2016-052-x
Mots-clés : 46L89, 43A07, 46H20, 46M10, 58B32, amenability, Arens regularity, co-amenability, locally compact quantum group, homological property 
Ghanei, Mohammad Reza; Nasr-Isfahani, Rasoul; Nemati, Mehdi. A Homological Property and Arens Regularity of Locally Compact Quantum Groups. Canadian mathematical bulletin, Tome 60 (2017) no. 1, pp. 122-130. doi: 10.4153/CMB-2016-052-x
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     title = {A {Homological} {Property} and {Arens} {Regularity} of {Locally} {Compact} {Quantum} {Groups}},
     journal = {Canadian mathematical bulletin},
     pages = {122--130},
     year = {2017},
     volume = {60},
     number = {1},
     doi = {10.4153/CMB-2016-052-x},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2016-052-x/}
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