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RB Yadav

Publications and source records attributed to RB Yadav.

12 recordsLinked to original sources
arXiv2026

Crossed Homomorphisms on associative superalgebras

In this paper, we introduce the notion of crossed homomorphisms on associative superalgebras. We show that crossed homomorphisms are precisely the Maurer--Cartan elements of a naturally associated graded Lie algebra. This characterization enables us to construct a cohomology theory of crossed homomorphisms. We then investigate formal deformations of crossed homomorphisms and derive the corresponding deformation equations. It is proved that the infinitesimal part of a formal deformation is a 1-cocycle in the associated cohomology, while the obstruction to extending a deformation of finite order is a 2-cocycle.

math.GM↗
arXiv2025

Characterization and Cohomology of Crossed Homomorphisms on Lie Superalgebras

In this article, we give a characterisation of crossed homomorphisms on Lie superalgebras as a Maurer-Cartan element of a graded Lie algebra. Using this characterisation we study cohomology of these crossed homomorphisms. As an application of this cohomology we study formal deformation of crossed homomorphisms. We show that linear deformations of these homomorphisms are characterised by one cocycles.

math.GM↗
arXiv2023

Cohomology and deformation of compatible Hom-Leibniz algebras

In this paper, we consider compatible Hom-Leibniz algebra where the Hom map twists the operations in the compatible system. We consider a suitably graded Lie algebra whose Maurer-Cartan elements characterize the structure of compatible Hom-Leibniz algebras. Using this, we study cohomology, infinitesimal deformations, the Nijenhuis operator, and their relation for compatible Hom-Leibniz algebras. Finally we see the cohomology of compatible Hom-Leibniz algebra with coefficients in an arbitrary representation.

math.RA↗
arXiv2023

Cohomology and deformations of compatible Leibniz algebras

In this paper we study a cohomology theory of compatible Leibniz algebra. We construct a graded Lie algebra whose Maurer-Cartan elements characterize the structure of compatible Leibniz algebras. Using this, we study cohomology, infinitisimal deformations, Nijenhuis operator and their relation for compatible leibniz algebras. Finally using cohomology of compatible Leibniz algebra with coefficients in an arbitrary representation we study the abelian extensions of compatible Leibniz algebra.

math.RA↗
arXiv2022

Equivariant Cohomology of Lie superalgebras

In this article, we give Maurer-Cartan characterizations of equivariant Lie superalgebra structures. We introduce equivariant cohomology and equivariant formal deformation theory of Lie superalgebras. As an application of equivariant cohomology we study the equivariant formal deformation theory of Lie superalgebras. As another application we characterize equivariant central extensions of Lie superalgebras using second equivariant cohomology. We give some examples of Lie superalgebras with an action of a group and equivariant formal deformations of a classical Lie superalgebras.

math.GM↗
arXiv2021

Cohomology and Deformation of Leibniz Superalgebras

In this article, we introduce a deformation cohomology of Leibniz superalgebras. Also, we introduce formal deformation theory of Leibniz superalgebras. Using deformation cohomology we study the formal deformation theory of Leibniz superalgebras.

math.RA↗
arXiv2020

Equivariant one-parameter deformations of Lie triple systems

In this article, we introduce equivariant formal deformation theory of Lie triple systems. We introduce an equivariant deformation cohomology of Lie triple systems and using this we study the equivariant formal deformation theory of Lie triple systems.

math.RA↗
arXiv2019

Equivariant one-parameter deformations of associative algebra morphisms

In this article, we introduce equivariant formal deformation theory of associative algebra morphisms. We introduce an equivariant deformation cohomology of associative algebra morphisms and using this we study the equivariant formal deformation theory of associative algebra morphisms.

math.GM↗
arXiv2018

Cohomology and deformations of module homorphisms

In this paper, we mainly focus on formal deformation theory of module homomorphisms. We first introduce the cohomology of module homomorphisms and study formal one-parameter deformation. We obtain some properties about obstructions. Then we give some examples of deformations of modules and module homomorphisms.

math.RA↗
arXiv2018

Conformal Riemannian morphisms between Riemannian manifolds

In this article we introduce conformal Riemannian morphisms. The idea of conformal Riemannian morphism generalizes the notions of an isometric immersion, a Riemannian submersion, an isometry, a Riemannian map and a conformal Riemannian map. We show that every injective conformal Riemannian morphism is an injective conformal immersion, and that on a connected manifold, every surjective conformal Riemannian morphism is a surjective conformal submersion, and every bijective conformal Riemannian morphism is a conformal map.

math.DG↗