Cohomology of Hom-Lie superalgebras and q-deformed Witt superalgebra

Abstract

The purpose of this paper is to define the representation and the cohomology of Hom-Lie superalgebras. Moreover we study Central extensions and provide as application the computations of the derivations and second cohomology group of q-deformed Witt superalgebra.

A classification of low dimensional multiplicative Hom-Lie superalgebras

“…Moreover, for˛¤ 0;ˇ¤ 0; ¤ 0; ¤ 0, the bracket can be simplified as (17). However, for formula (17) Proof.…”

“…In particular, Cao and Luo [16] proved that there were only the trivial Hom-Lie superalgebras on the finite-dimensional simple Lie superalgebras. The representation theory and the cohomology theory of Hom-Lie superalgebras were studied in [17]. In [18], some infinite-dimensional Hom-Lie superalgebras were constructed, induced by affinizations of the Hom-Balinskii-Novikov superalgebras and Hom-Novikov superalgebras.…”

Constructions and Cohomology of Hom–Lie Color Algebras

“…We extend to Hom-Lie color algebras, the concept of -module introduced in [3,10,32], and then define a family of cohomology complexes for Hom-Lie color algebras.…”

“…Hom-Lie color algebras were studied first in [36]. In the particular case of Hom-Lie superalgebras, a cohomology theory was provided in [3], see also [28]. Notice that for Hom-Lie algebras, cohomology was described in [2,20,32] and representations also in [10].…”

Generalized Derivations of BiHom-Lie Algebras

“…Recently, Hom-Lie algebras were studied in refs. [8,9]. More applications of the Hom-Lie algebras, Hom-algebras and Hom-Lie superalgebras can be found in refs.…”