Deformations of filiform Lie algebras and superalgebras
Expanding previous work on the subject, this paper deals with deformations of the so-called model filiform Lie superalgebra \(L^{n,m}\) that extends naturally the filiform Lie algebra \(L_{n}\). The specific objective of the paper is the analysis and classification of deformations based on cocycles of the space \(Z^{2}(L^{n,m},Z^{2}(L^{n,m})\cap \Hom(L_{n}\wedge L_{n},L_{n})\). This enables to characterize the cocycles of \(L_{n}\) that are also cocycles at the superalgebra level. An algorithm that allows explicit determination of the corresponding bases of cocycles up to \(n\leq 10\) is given.
scientific article; zbMATH DE number 5736303