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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…