1 citations · 1 across the 12 of their papers we have counts for
12 papers
Nijenhuis Lie -algebras
Apurba Das
In this paper, we first introduce Nijenhuis Lie 2-algebras as the categorification of Nijenhuis Lie algebras. We prove that the category of Nijenhuis Lie 2-algebras is equivalent t…
Difference -algebras and difference -algebras
Apurba Das
A difference operator on an associative algebra is an algebraic abstraction of the forward and backward difference operators. In this paper, we first introduce difference operators…
Factorizations, classifying complements problem and deformation maps for Lie-Yamaguti algebras
Apurba Das
A Lie-Yamaguti algebra is a non-associative algebraic structure that generalizes both Lie algebras and Lie triple systems. We first consider the factorization problem for Lie-Yamag…
Frölicher-Nijenhuis bracket and derived bracket associated to a nonsymmetric operad with multiplication
Anusuiya Baishya, Apurba Das
This paper aims to construct two graded Lie algebras associated with a nonsymmetric operad with multiplication. Maurer-Cartan elements of these graded Lie algebras correspond respe…
Cohomology theory of Nijenhuis Lie algebras and (generic) Nijenhuis Lie bialgebras
Apurba Das
The aim of this paper is twofold. In the first part, we define the cohomology of a Nijenhuis Lie algebra with coefficients in a suitable representation. Our cohomology of a Nijenhu…
Non-abelian cohomology of Nijenhuis Lie algebras and the inducibility of automorphisms and derivations
Apurba Das
In this paper, we first introduce the non-abelian cohomology group of a Nijenhuis Lie algebra with values in another Nijenhuis Lie algebra and show that it parametrizes the isomorp…
Deformation cohomology of Nijenhuis algebras and applications to extensions, inducibility of automorphisms and homotopy algebras
Apurba Das
Our primary aim in this paper is to introduce and study the cohomology of a Nijenhuis operator and of a Nijenhuis algebra. Our cohomology of a Nijenhuis algebra controls the simult…
Cup product, Frölicher-Nijenhuis bracket and the derived bracket associated to Hom-Lie algebras
Anusuiya Baishya, Apurba Das
In this paper, we introduce some new graded Lie algebras associated with a Hom-Lie algebra. At first, we define the cup product bracket and its application to the deformation theor…
Higher structures for Lie -pseudoalgebras
Apurba Das
Let be a cocommutative Hopf algebra. The notion of Lie -pseudoalgebra is a multivariable generalization of Lie conformal algebras. In this paper, we study some higher struct…
Representations and cohomology of a matched pair of Lie algebras, and -algebras
Anusuiya Baishya, Apurba Das
The notion of a matched pair of Lie algebras was introduced in the study of Lie bialgebras and Poisson-Lie groups. In this paper, we introduce representations and cohomology of a m…
Nijenhuis deformations of Poisson algebras and -manifold algebras
Anusuiya Baishya, Apurba Das
The notion of pre-Poisson algebras was introduced by Aguiar in his study of zinbiel algebras and pre-Lie algebras. In this paper, we first introduce NS-Poisson algebras as a genera…
Non-abelian cohomology of Lie -pseudoalgebras and inducibility of automorphisms
Apurba Das
The notion of Lie -pseudoalgebra is a higher-dimensional analogue of Lie conformal algebras. In this paper, we classify the equivalence classes of non-abelian extensions of a Li…