A Kind Of New Generalized Derivations Of Lie Algebras

Let g be a finite-dimensional Lie algebra over an algebraically closed field F of char-acteristic zero.The present thesis is devoted to a systematic study on(σ,τ)-derivations,where σ,τ are automorphisms of g.We mainly study properties of(σ,τ)-derivations of g and connections with other generalized derivations of g.Give a subgroup G≤Aut(g),we also study the interiors of G-derivations of g and compute the corresponding Hilbert series for the case G is a cyclic group.In particular,we apply a method from commutative algebra to explicitly calculate(σ,τ)-derivations of sl2(C)for three families of inner auto-morphisms,and completely determine the geometric structures of the corresponding affine varieties.