Cohomology and deformations of the infinite dimensional filiform Lie algebra m_0

Details Cohomology and deformations of the infinite dimensional filiform Lie algebra m_0 Cohomology and deformations of the infinite dimensional filiform Lie algebra m_0

2007-03-13

arxiv.org/abs/math/0703383v2

Mathematics

Representation Theory

25 pages

Scientific paper

Denote m_0 the infinite dimensional N-graded Lie algebra defined by basis e_i, i>= 1 and relations [e_1,e_i] = e_(i+1) for all i>=2. We compute in this article the bracket structure on H1(m_0,m_0), H2(m_0,m_0) and in relation to this, we establish that there are only finitely many true deformations of m_0 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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