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Representation Theory

Published by the American Mathematical Society, the Representation Theory (ERT) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-4165

The 2020 MCQ for Representation Theory is 0.7.

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Module extensions over classical Lie superalgebras
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by Edward S. Letzter PDF
Represent. Theory 3 (1999), 354-372 Request permission


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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Additional 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