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Finitude de l’homologie de certains modules de dimension finie sur une super algèbre de Lie. (Finiteness of the homology of some finite dimensional vector spaces on a Lie superalgebra.). (French) Zbl 0974.17024

Summary: We give an hypothesis to make sure that the homology of a Lie superalgebra operating on a finite dimensional super vector space is finite.
Especially the author considers examples of simple Lie superalgebras with reductive even parts: \({\mathfrak o}{\mathfrak s}{\mathfrak p}(m,2n)\), \({\mathfrak s}{\mathfrak l}(m,n)\), \(m\neq n\), \(G(3)\), \(F(4)\), and \(D(2,1,\lambda)\). She describes the cohomology of \(G(3)\), \(F(4)\), and \(D(2,1,\lambda)\) with coefficients in the trivial module.

MSC:

17B55 Homological methods in Lie (super)algebras
17B70 Graded Lie (super)algebras
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References:

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