STRUCTURE OF SYMPATHETIC LIE SUPERALGEBRAS

Sympathetic Lie superalgebras are defined and some classical properties of sympathetic Lie superalgebras are given. Among the main results, we prove that any Lie superalgebra L contains a maximal sympathetic graded ideal and we obtain some properties about sympathetic decomposition. More specifically, we study a general sympathetic Lie superalgebra L with graded ideals I, J and S such that L = I circle plus J and L/S is a sympathetic Lie superalgebra, and we obtain some properties of L/S. Furthermore, under certain assumptions on L we prove that the derivation algebra Der(L) is sympathetic and that if in addition L is indecomposable, then Der(L) is simply sympathetic.