Cohomology of graded Lie algebras of maximal class (original) (raw)

On the cohomology based on the generalized representations of nnn-Lie Algebras

Cornell University - arXiv, 2022

In the present paper, we define the new class of representation on n-Lie algebra that is called as generalized representation. We study the cohomology theory corresponding to generalized representations of n-Lie algebras and show its relation with the cohomology corresponding to the usual representations. Furthermore, we provide the computation for the low dimensional cocycles.

Cohomology and deformations of the infinite dimensional filiform Lie algebra m_0

2007

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.

Massey Products in Graded Lie Algebra Cohomology

2005

We discuss Massey products in a N-graded Lie algebra cohomology. One of the main examples is so-called ”positive part” L1 of the Witt algebra W. Buchstaber conjectured that H ∗ (L1) is generated with respect to non-trivial Massey products by H¹(L1). Feigin, Fuchs and Retakh represented H ∗ (L1) by trivial Massey products and the second part of the Buchstaber conjecture is still open. We consider the associated graded algebra m0 of L1 with respect to the filtration by its descending central series and prove that H ∗ (m0) is generated with respect to non-trivial Massey products by H¹(m0).

Cohomology and deformations of the infinite dimensional filiform Lie algebra m_2

2007

Denote _2 the infinite dimensional -graded Lie algebra defined by the basis e_i for i≥ 1 and by relations [e_1,e_i]=e_i+1 for all i≥ 2, [e_2,e_j]=e_j+2 for all j≥ 3. We compute in this article the bracket structure on H^1(_2,_2), H^2(_2,_2) and in relation to this, we establish that there are only finitely many true deformations of _2 in each weight by constructing them explicitely. It turns out that in weight 0 one gets as non-trivial deformation only one formal non-converging deformation.

On the cohomology of the Lie algebraL2

Pacific Journal of Mathematics

ON THE COHOMOLOGY OF THE LIE ALGEBRA L 2 ALICE FIALOWSKI We compute the 0-, 1-, and 2-dimensional homology of the vector field Lie algebra L 2 with coefficients in the modules JF λμ , and conjecture that the higher dimensional homology for any λ and μ is zero. We completely compute the 0-and 1-dimensional homology with coefficients in the more complicated modules F\^μ. We also give a conjecture on this homology in any dimension for generic λ and μ.

Graded Lie algebras of maximal class, III

Journal of Algebra, 2005

We describe the isomorphism classes of infinite-dimensional N-graded Lie algebras of maximal class generated by their first homogeneous component over fields of characteristic two. This complements the analogous work by Caranti and Newman in the odd characteristic case.