Let $A$ be an abelian topological group and $B$ a trivial topological $A$-module. In this paper we define the second bilinear cohomology with a trivial coefficient. We show that every abelian group can be embedded in a central extension of abelian groups with bilinear cocycle. Also we show that in the category of locally compact abelian groups a central extension with a continuous section can b...

let $a$ be an abelian topological group and $b$ a trivial topological $a$-module. in this paper we define the second bilinear cohomology with a trivial coefficient. we show that every abelian group can be embedded in a central extension of abelian groups with bilinear cocycle. also we show that in the category of locally compact abelian groups a central extension with a continuous section can b...

We consider the aff(1)-module structure on the spaces of bilinear differential operators acting on the spaces of weighted densities. We compute the first differential cohomology of the Lie superalgebra aff(1) with coefficients in space Dλ,ν;µ of bilinear differential operators acting on weighted densities. We study also the super analogue of this problem getting the same results.

The purpose of this paper is to give a characterization families expander graphs via right-angled Artin groups. We prove that sequence simplicial [Formula: see text] forms family if and only certain natural mini-max invariant arising from the cup product in cohomology rings groups agrees with Cheeger constant graphs, thus allowing us characterize cohomology. This result proved more general fram...

In this work we consider the moduli space of all noncommutative metric Lie algebras, having a nondegenerate symmetric invariant bilinear form, over $\mathbb C$ and R$ up to dimension 5 algebras in 6. We introduce cyclic reduced cohomology identify their deformations.

Let V be an even dimensional vector space over a field K of characteristic 2 equipped with a non-degenerate alternating bilinear form f . The divided power algebra DV is considered as a complex with differential defined from f . We examine the cohomology modules as representations of the corresponding symplectic group.

1 Hodge structures 3 1.1 The Hodge decomposition . . . . . . . . . . . . . . . . . . . . . . . . 3 1.1.1 The Frölicher spectral sequence . . . . . . . . . . . . . . . . . 3 1.1.2 Hodge filtration and Hodge decomposition . . . . . . . . . . . 6 1.1.3 Hodge structures . . . . . . . . . . . . . . . . . . . . . . . . 7 1.2 Morphisms of Hodge structures . . . . . . . . . . . . . . . . . . . . . 10 1...