Topologically projective, injective and flat modules of harmonic analysis

We study homologically trivial modules of harmonic analysis on a locally compact group $G$. For $L_1(G)$- and $M(G)$-modules $C_0(G)$, $L_p(G)$ and $M(G)$ we give criteria for metric and topological projectivity, injectivity and flatness. In most cases, modules with these properties must be finite-dimensional.
Bibliography: 18 titles.