Geodesic
On relative homological dimension of group algebras of locally compact groups
Izvestiya. Mathematics , Tome 7 (1973) no. 2, pp. 307-317

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Let $G$ be a noncompact, locally compact group with an invariant mean, $L_1(G)$ its group algebra, and $I$ the ideal of $L_1(G)$ formed by those functions whose Haar integral is zero. In this paper it is shown that the (relative) homological dimension of the Banach $L_1(G)$-module $L_1(G)/I$ is infinite. By the same token the (relative) global dimension of the Banach algebra $L_1(G)$ is also infinite. This result is then applied to the study of cohomology groups of a locally compact group with coefficients in Banach $G$-modules. 
@article{IM2_1973_7_2_a3,
     author = {M. V. Sheinberg},
     title = {On relative homological dimension of group algebras of locally compact groups},
     journal = {Izvestiya. Mathematics },
     pages = {307--317},
     publisher = {mathdoc},
     volume = {7},
     number = {2},
     year = {1973},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1973_7_2_a3/}
}
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M. V. Sheinberg. On relative homological dimension of group algebras of locally compact groups. Izvestiya. Mathematics , Tome 7 (1973) no. 2, pp. 307-317. http://geodesic.mathdoc.fr/item/IM2_1973_7_2_a3/