2022/07/23 by Nandi, Nupur, Padhan, Rudra Narayan
#FOS: Mathematics #Rings and Algebras (math.RA)
paper · doi:10.48550/arxiv.2207.11443
The main object of study of this paper is the notion of 3-Lie superalgebras with superderivations. We consider a representation (Φ,P) of a 3-Lie superalgebra Q on P and construct first-order cohomologies by using superderivations of P,Q which induces a Lie superalgebra TΦ and its representation Ψ. Then we consider abelian extensions of 3-Lie superalgebras of the form 0→ P\hookrightarrow L→ Q→ 0 with [P,P,L]=0 and construct an obstruction class to extensibility of a compatible pair of superderivation. Moreover we prove that a pair of superderivation is extensible if and only if its obstruction class is trivial under some suitable conditions.