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. 
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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/

[1] Khelemskii A. Ya., “O gomologicheskoi razmernosti normirovannykh modulei nad banakhovymi algebrami”, Matem. sb., 81(123) (1970), 430–444

[2] Khelemskii A. Ya., “Ob odnom metode vychisleniya i otsenki globalnoi gomologicheskoi razmernosti banakhovykh algebr”, Matem. sb., 87(129):1 (1972), 122–135 | MR | Zbl

[3] Kamowitz G., “Cohomology Groups of Commutative Banach Algebres”, Trans. Amer. Math. Soc., 102:2 (1962), 352–372 | DOI | MR | Zbl

[4] Khelemskii A. Ya., “Globalnaya razmernost funktsionalnoi banakhovoi algebry otlichna ot 1”, Funktsionalnyi analiz, 6:2 (1972), 95–96

[5] Greenleaf F., Invariant Means on Topological Groups and their Applications, Van Nostand, New York, 1969 | MR | Zbl

[6] Johnson B., Approximate Diagoneles and Cohomology of Certain Annigilator Banach Algebres, Rotaprint, Yale University Press, 1971

[7] Khelemskii A. Ya., “Lokalno kompaktnaya abeleva gruppa s trivialnymi dvumernymi kogomologiyami kompaktna”, Dokl. AN SSSR, 203:5 (1972), 1004–1008

[8] Johnson B., Cohomology in Banach Algebres, Mem. Amer. Math. Soc., 127, 1972 | MR | Zbl

[9] Rieffel M., “Induced Banach Representations of Banach Algebres and Locally Compact Groups”, J. of Func. An., 1:4 (1967), 443–491 | DOI | MR | Zbl

[10] Hewitt E., “The ranges of certain convolution operators”, Math. Scand., 15:2 (1964), 147–155 | MR | Zbl

[11] Sheinberg M. V., “Otnositelno in'ektivnye moduli nad banakhovymi algebrami”, Vestn. Mosk. un-ta, 1971, no. 3, 53–58 | Zbl

[12] Sheffer X., Lineinye topologicheskie prostranstva, Mir, M., 1971

[13] Sheinberg M. V., “Gomologicheskie svoistva zamknutykh idealov, obladayuschikh ogranichennoi approksimativnoi edinitsei”, Vestn. Mosk. un-ta, 1972, no. 4, 39–45

[14] Khelemskii A. Ya., “Periodicheskoe proizvedenie modulei nad banakhovymi algebrami”, Funktsionalnyi analiz, 5:1 (1971), 95–96 | MR

[15] Kargan A., Eilenberg S., Gomologicheskaya algebra, IL, M., 1960