Resumen de On the Betti numbers of filiform Lie algebras over fields of characteristic two

Ioannis Tsartsaflis

• An n-dimensional Lie algebra g over a field F of characteristic two is said to be of Vergne type if there is a basis e1,…,en such that [e1,ei]=ei+1 for all 2≤i≤[ei,ej]n−1 and =ci,jei+j for some ci,j∈F for all i,j≥2 with i+j≤n. We define the algebra m0 by its nontrivial bracket relations:

  [e1,ei]=ei+1, 2≤i≤n−1, and the algebra m2: [e1,ei]=ei+1, 2≤i≤[e2,ej]n−1, =ej+2, 3≤j≤n−2. We show that, in contrast to the corresponding real and complex cases, m0(n) and m2(n) have the same Betti numbers. We also prove that for any Lie algebra of Vergne type of dimension at least 5, there exists a non-isomorphic algebra of Vergne type with the same Betti numbers.