In this paper, we present some basic properties concerning the derivation algebra Der (T), the quasiderivation algebra QDer (T) and the generalized derivation algebra GDer (T) of a Lie triple system T, with the relationship Der (T) ⊆ QDer (T) ⊆ GDer (T) ⊆ End (T). Furthermore, we completely determine those Lie triple systems T with condition QDer (T) = End (T). We also show that the quasiderivations of T can be embedded as derivations in a larger Lie triple system.
The paper studies nilpotent -Lie superalgebras over a field of characteristic zero. More specifically speaking, we prove Engel’s theorem for -Lie superalgebras which is a generalization of those for -Lie algebras and Lie superalgebras. In addition, as an application of Engel’s theorem, we give some properties of nilpotent -Lie superalgebras and obtain several sufficient conditions for an -Lie superalgebra to be nilpotent by using the notions of the maximal subalgebra, the weak ideal and the...
We construct a family of non-weight modules which are free -modules of rank 2 over the super Schrödinger algebra in -dimensional spacetime. We determine the isomorphism classes of these modules. In particular, free -modules of rank 2 over are also constructed and classified. Moreover, we obtain the sufficient and necessary conditions for such modules to be simple.
Download Results (CSV)