Abstract
This paper is primarily devoted to studying (?, ?)-derivations of finite-dimensional Lie superalgebras over an algebraically closed field F. We research some properties of (?, ?)-derivations and the relationship between the (?, ?)-derivations and other generalized derivations. Under certain conditions, a left-multiplication structure concerned with (?, ?)-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.
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