Restricted Lie superalgebras and their universal enveloping algebras

Let L be a restricted Lie superalgebra with restricted enveloping algebra u(L). In the second chapter, we consider the augmentation ideal of u(L) denoted by ou(L). First, o u(L) is nilpotent if and only if L is a finite dimensional, nilpotent restricted Lie superalgebra of finite exponent. We also characterize those restricted Lie superalgebras which are residually "nilpotent and of finite exponent," in other words, there exists a restricted ideal I ◃p L such that, x ∉ I and L/I is nilpotent and of finite exponent. Also, there is a bound on t(L), the nilpotenct index of ou(L). Upper Lie nippotence is also discussed. Specifically, a bound is found for the upper Lie dimension of u(L). Next, we categorize when an enveloping algebra, u(L), is upper Lie nilpotent.