<abstract><p>The main purpose of this paper is to provide a full cohomology Hom-pre-Lie algebra with coefficients in given representation. This new type exploits strongly the Hom-type structure and fits perfectly simultaneous deformations multiplication homomorphism defining algebra. Moreover, we show that its second group classifies abelian extensions by representation.</p>&l...

We show how to gauge the set of raising and lowering generators of an arbitrary Lie algebra. We consider SU(N) as an example. The nilpotency of the BRST charge requires constraints on the ghosts associated to the raising and lowering generators. To remove these constraints we add further ghosts and we need a second BRST charge to obtain nontrivial cohomology. The second BRST operator yields a g...

the aim of this paper is to study the $(alpha‎, ‎gamma)$-prolongation of central extensions‎. ‎we obtain the obstruction theory for $(alpha‎, ‎gamma)$-prolongations and classify $(alpha‎, ‎gamma)$-prolongations thanks to low-dimensional cohomology groups of groups‎.

0.1. In this paper we construct a number of geometrically meaningful 1– and 2– cocycles of infinite dimensional Lie groups and Lie algebras. The groups are groups of diffeomorphisms of smooth manifolds and their subgroups, such as the group of symplectomorphisms of a symplectic manifold; the Lie algebras are algebras of vector fields. Coefficient spaces of the cocycles are spaces of various ten...

In this paper, we introduced the concept of crossed modules for Hom–Lie antialgebras. It is proved that category antialgebras and [Formula: see text]-Hom–Lie are equivalent to each other. The relationship between extension third cohomology group investigated.

We describe a method for computing presentations of cohomology rings of small finite p-groups. The description differs from other accounts in the literature in two main respects. First, we suggest some techniques for improving the efficiency of the obvious linear algebra approach to computing projective resolutions over a group algebra. Second, we use an implementation of the multiplicative str...

In the work of Rostami et al., Bogomolov multiplier a Lie algebra L over field Ω is defined as particular factor subalgebra exterior product L∧L. If finite dimensional, we identify this object certain subgroup second cohomology group H2(L,Ω) by deriving Hopf-Type formula. As an application, affirmatively answer two questions posed Kunyavskiĭ regarding invariance under isoclinism algebras and ex...

Various aspects of the de Rham cohomology of Hopf algebras are discussed. In particular, it is shown that the de Rham cohomology of an algebra with the differentiable coaction of a cosemisimple Hopf algebra with trivial 0-th cohomology group, reduces to the de Rham cohomology of (co)invariant forms. Spectral sequences are discussed and the van Est spectral sequence for Hopf algebras is introduc...

Introduced by Borel in the late 1950’s, equivariant cohomology encodes information about how the topology of a space interacts with a group action. Quite some time passed before algebraic geometers picked up on these ideas, but in the last twenty years, equivariant techniques have found many applications in enumerative geometry, Gromov-Witten theory, and the study of toric varieties and homogen...