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Search: MSC category 46M10 ( Projective and injective objects [See also 46A22] )

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1. CMB Online first

Ghanei, Mohammad Reza; Nasr-Isfahani, Rasoul; Nemati, Mehdi
A homological property and Arens regularity of locally compact quantum groups
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
Categories:46L89, 43A07, 46H20, 46M10, 58B32

2. CMB 2004 (vol 47 pp. 445)

Pirkovskii, A. Yu.
Biprojectivity and Biflatness for Convolution Algebras of Nuclear Operators
For a locally compact group $G$, the convolution product on the space $\nN(L^p(G))$ of nuclear operators was defined by Neufang \cite{Neuf_PhD}. We study homological properties of the convolution algebra $\nN(L^p(G))$ and relate them to some properties of the group $G$, such as compactness, finiteness, discreteness, and amenability.

Categories:46M10, 46H25, 43A20, 16E65

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