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Cohomology of some nilpotent Lie algebras. (Russian) Zbl 0682.17008
Let \(\mathfrak g\) be a complex finite-dimensional simple Lie algebra and \(\mathfrak n\) be the nilradical of a parabolic subgroup of \(\mathfrak g\). In the paper the cohomology spaces \(H^ 1(\mathfrak n;\mathfrak n)\) and \(H^ 2(\mathfrak n;\mathfrak n)\) are described. The description of \(H^ 2(\mathfrak n;\mathfrak n)\) is reduced to the study of the space \(H^ 1(\mathfrak n;\mathfrak g/\mathfrak n)\). In the proofs B. Kostant ’s results are used [Ann. Math. (2) 74, 329–387 (1961; Zbl 0134.03503)]. As an application, the manifold of Lie structures of a finite-dimensional vector space is studied.

MSC:
17B56 Cohomology of Lie (super)algebras
17B30 Solvable, nilpotent (super)algebras
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