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Cohomologies of the Lie algebra of vector fields with coefficients in a trivial unitary representation. (English. Russian original) Zbl 0299.58002
Funct. Anal. Appl. 6, 21-30 (1972); translation from Funkts. Anal. Prilozh. 6, No. 1, 24-36 (1972).

MSC:
58A15 Exterior differential systems (Cartan theory)
17B55 Homological methods in Lie (super)algebras
17B56 Cohomology of Lie (super)algebras
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References:
[1] H. Weyl, The Classical Groups, Princeton, New Jersey (1946). · Zbl 1024.20502
[2] I. M. Gel’fand and D. B. Fuks, ”Cohomology of the Lie algebra of tangent vector fields of a smooth manifold,” Funktsional. Analiz i Ego Prilozhen.,3, No. 3, 32-52 (1969).
[3] I. M. Gel’fand and D. B. Fuks, ”Cohomology of the Lie algebra of formal vector fields,” Izv. Akad. Nauk SSSR, Seriya Matem.,34, 322-337 (1970).
[4] I. M. Gel’fand and D. B. Fuks, ”Cohomology of the Lie algebra of vector fields with nontrivial coefficients,” Funktsional. Analiz i Ego Prilozhen.,4, No. 3, 10-25 (1970).
[5] I. M. Gel’fand and D. B. Fuks, ”Cohomology of the Lie algebra of tangent vector fields of a smooth manifold, II,” Funktsional. Analiz i Ego Prilozhen.,4, No. 2, 23-31 (1970).
[6] I. M. Gel’fand and D. B. Fuks, ”Cohomology of the Lie algebra of smooth vector fields,” Dokl. Akad. Nauk SSSR,190, No. 6, 1268-1270 (1970).
[7] A. Lichnerowicz, Theory of Global Connections and Holonomy Groups [Russian translation], IL, Moscow (1960).
[8] M. V. Losik, ”Cohomology of infinite-dimensional Lie algebras of vector fields,” Funktsional. Analiz i Ego Prilozhen.,4, No. 2, 43-53 (1970). · Zbl 0212.28002
[9] L. S. Pontryagin, ”Certain topological invariants of closed Riemannian manifolds,” Izv. Akad. Nauk SSSR, Seriya Matem.,13, 125-162 (1949).
[10] J. Schwartz, Differential Geometry and Topology [Russian translation], Mir, Moscow (1970). · Zbl 0195.53102
[11] H. Cartan, ”The transgression on a Lie group and a principal fiber space,” in: Coll. de Topologie, Bruxelles, 1950, Paris (1951), pp. 57-72.
[12] J. L. Koszul, ”A type of differential algebra compatible with the transgression,” in: Coll. de Topologie, Bruxelles, 1950, Paris (1951), pp. 73-81.
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