Cohomology and deformations of the infinite dimensional filiform Lie algebra m0
Abstract
Denote m0 the infinite dimensional N-graded Lie algebra defined by basis ei, i>= 1 and relations [e1,ei] = e(i+1) for all i>=2. We compute in this article the bracket structure on H1(m0,m0), H2(m0,m0) and in relation to this, we establish that there are only finitely many true deformations of m0 in each nonpositive weight, by constructing them explicitely. It turns out that in weight 0 one gets exactly the other two filiform Lie algebras.
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