A complete description of all the infinitesimal deformations of the Lie superalgebra \(L^{n,m}\)
The aim of this work is to complete the description and classification of infinitesimal deformations of the model Lie superalgebra \(L^{n,m}\) given by the brackets \([X_{0},X_{i}] = X_{i+1}\) (\(1\leq i \leq n-1\)) and \([X_{0},Y_{j}] = Y_{j+1}\) (\(1\leq j \leq m-1\)) over a basis \(X_{0},X_{1},\dots ,X_{n},Y_{1},\dots ,Y_{m}\). In analogy with the case of Lie algebras, it turns out that this superalgebra is the main structure from which all filiform superalgebras can be derived by means of infinitesimal deformations. The authors give an explicit decomposition of the cohomology space \(Z^{2}(L^{n,m},Z^{2}(L^{n,m})\) and bases of all its components.
scientific article; zbMATH DE number 5655064