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# 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.
 MSC Classifications: 46M10 - Projective and injective objects [See also 46A22] 46H25 - Normed modules and Banach modules, topological modules (if not placed in 13-XX or 16-XX) 43A20 - $L^1$-algebras on groups, semigroups, etc. 16E65 - Homological conditions on rings (generalizations of regular, Gorenstein, Cohen-Macaulay rings, etc.)