MODULE EXTENSIONS OVER CLASSICAL LIE SUPERALGEBRASEdward

We study certain ltrations of indecomposable injective modules over classical Lie superalgebras, applying a general approach for noetherian rings developed by Brown, Jategaonkar, Lenagan, and Warreld. To indicate the consequences of our analysis, suppose that g is a complex classical simple Lie superalgebra and that E is an indecomposable injective g-module with nonzero (and so necessarily simple) socle L. (Recall that every essential extension of L, and in particular every nonsplit extension of L by a simple module, can be formed from g-subfactors of E.) A direct transposition of the Lie algebra theory to this setting is impossible. However, we are able to present a nite upper bound, easily calculated and dependent only on g, for the number of isomorphism classes of simple highest weight g-modules appearing as g-subfactors of E.