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Algèbre enveloppante et cohomologie des bimodules de Malcev. (Enveloping algebra and cohomology of Malcev bimodules). (French) Zbl 0607.17013
Following the ideas of N. Jacobson [Structure and representations of Jordan algebras (1968; Zbl 0218.17010)], an associative algebra E(A) is defined for every Malcev algebra A, so that the modules for A are precisely the right modules for E(A). In the same way, another associative algebra S(A) is defined, such that the Lie modules for A are the right modules for S(A) (up to isomorphism, S(A) is the universal enveloping algebra of the algebra A/J(A,A,A) ). In spite of the Remark 1.6 in this paper, if A is a Lie algebra then E(A) is not isomorphic to S(A) in general. For instance S(sl(2,F)) is a proper quotient of E(sl(2,F)). The cohomology of the modules for Malcev algebras is studied by using these associative algebras.
Reviewer: A.Elduque
17D10 Mal’tsev rings and algebras