7 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…