Nilradicals of parabolic subalgebras admitting symplectic structures

In this paper we describe all the nilradicals of parabolic subalgebras of split real simple Lie algebras admitting symplectic structures. The main tools used to obtain this list are Kostant's description of the highest weight vectors (hwv) of the cohomology of these nilradicals and some necessary conditions obtained for the $\mathfrak g$-hwv's of $H^2(\mathfrak n)$ for a finite dimensional real symplectic nilpotent Lie algebra $\mathfrak n$ with a reductive Lie subalgebra of derivations $\mathfrak g$ acting on it

On generalized G2-structures and T-duality

This is a short note on generalized G2-structures obtained as a consequence of a T-dual construction given in del Barco et al. (2017). Given classical G2-structure on certain seven dimensional manifolds, either closed or co-closed, we obtain integrable generalized G2-structures which are no longer a usual one, and with non-zero three form in general. In particular we obtain manifolds admitting closed generalized G2-structures not admitting closed (usual) G2-structures.Fil: del Barco, Viviana Jorgelina. Universidade Estadual de Campinas; Brasil. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Rosario; Argentina. Universidad Nacional de Rosario. Facultad de Ciencias Exactas, Ingeniería y Agrimensura; ArgentinaFil: Grama, Lino. Universidade Estadual de Campinas; Brasi

On a spectral sequence for the cohomology of a nilpotent Lie algebra

Given a nilpotent Lie algebra we construct a spectral sequence which is derived from a filtration of its Chevalley-Eilenberg differential complex and converges to the Lie algebra cohomology of. The limit of this spectral sequence gives a grading for the Lie algebra cohomology, except for the cohomology groups of degree 0, 1, dim-1 and dim as we shall prove. We describe the spectral sequence associated to a nilpotent Lie algebra which is a direct sum of two ideals, one of them of dimension one, in terms of the spectral sequence of the co-dimension one ideal. Also, we compute the spectral sequence corresponding to each real nilpotent Lie algebra of dimension less than or equal to six.Fil: del Barco, Viviana Jorgelina. Universidad Nacional de Rosario. Facultad de Ciencias Exactas Ingeniería y Agrimensura. Escuela de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentin