Automorphisms of toroidal Lie superalgebras

We give a detailed description of the algebraic group Aut(g) of automorphisms of a simple finite dimensional Lie superalgebra g over an algebraically closed field k of characteristic 0. We also give a description of the group of automorphisms of the k-Lie superalgebra $g \otimes_k R$ whenever R is a Noetherian domain with trivial Picard group.Comment: 20 pages, contains some corrections and addition

Cuspidal representations of sl(n+1)

In this paper we study the subcategory of cuspidal modules of the category of weight modules over the Lie algebra sl(n+1). Our main result is a complete classification and explicit description of the indecomposable cuspidal modules.Comment: 31 pages, corrections added, to appear in Adv. Mat

Bounded highest weight modules of q(n)

A classification of the simple highest weight bounded modules of the queer Lie superalgebras q(n) is obtained. To achieve this classification we introduce a new combinatorial tool - the star action. Our result leads in particular to a classification of all simple weight q(n)-modules.Comment: 40 pages, some corrections made to the earlier version. To appear in IMR