On (σ, τ)-derivations of Lie superalgebras

This paper is primarily devoted to studying (sigma, tau)-derivations of finite-dimensional Lie super -algebras over an algebraically closed field F. We research some properties of (sigma, tau)-derivations and the relationship between the (sigma, tau)-derivations and other generalized derivations. Under certain conditions, a left-multiplication structure concerned with (sigma, tau)-derivations can induces a left-symmetric superalgebra structure. Let L be a Lie superalgebra, we give a subgroup G of Aut(L), exploiting fundamental properties, we introduce and analyze their interiors, especially focusing on the rationality of the corresponding Hilbert series when G is a cyclic group.