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Representation Theory

Published by the American Mathematical Society since 1997, this electronic-only journal is devoted to research in representation theory and seeks to maintain a high standard for exposition as well as for mathematical content. All articles are freely available to all readers and with no publishing fees for authors.

ISSN 1088-4165

The 2020 MCQ for Representation Theory is 0.71.

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Module extensions over classical Lie superalgebras
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by Edward S. Letzter
Represent. Theory 3 (1999), 354-372
Published electronically: October 5, 1999


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 $\mathfrak {g}$ is a complex classical simple Lie superalgebra and that $E$ is an indecomposable injective $\mathfrak {g}$-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 $\mathfrak {g}$-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 $\mathfrak {g}$, for the number of isomorphism classes of simple highest weight $\mathfrak {g}$-modules appearing as $\mathfrak {g}$-subfactors of $E$.
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Bibliographic Information
  • Edward S. Letzter
  • Affiliation: Department of Mathematics, Texas A&M University, College Station, Texas 77843
  • MR Author ID: 113075
  • Email:
  • Received by editor(s): November 20, 1998
  • Received by editor(s) in revised form: July 14, 1999
  • Published electronically: October 5, 1999
  • Additional Notes: This research was partially supported by grants from the National Science Foundation.
  • © Copyright 1999 American Mathematical Society
  • Journal: Represent. Theory 3 (1999), 354-372
  • MSC (1991): Primary 16P40, 17A70; Secondary 17B35
  • DOI:
  • MathSciNet review: 1711503