1999/05/10 by Edward S. Letzter, E. S. Letzter, Letzter, E. S.
Mathematics · #Advanced Topics in Algebra #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Quantum Algebra (math.QA) #Representation Theory (math.RT) #Rings and Algebras (math.RA) #math.QA #math.RA #math.RT
paper · pdf · doi:10.48550/arxiv.math/9905057
20 pages
arxiv created 1999/05/10 · openalex publication_date 1999/05/10 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study certain filtrations of indecomposable injective modules over classical Lie superalgebras, applying a general approach for noetherian rings developed by Brown, Jategaonkar, Lenagan, and Warfield. 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 finite 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.