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Cohomology and deformations of the infinite dimensional filiform Lie algebra m_0

Alice Fialowski·Friedrich Wagemann
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Abstract

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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Alice Fialowski, Friedrich Wagemann. 2007-03-13. Cohomology and deformations of the infinite dimensional filiform Lie algebra m_0. https://arxiv.org/abs/math/0703383

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