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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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The five exceptional simple Lie superalgebras of vector fields and their fourteen regradings
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by Irina Shchepochkina
Represent. Theory 3 (1999), 373-415
Published electronically: October 13, 1999


The five simple exceptional complex Lie superalgebras of vector fields are described. One of them, $\mathfrak {fas}$, is new; the other four are explicitly described for the first time. All nonisomorphic maximal subalgebras of finite codimension of these Lie superalgebras, i.e., all other realizations of these Lie superalgebras as Lie superalgebras of vector fields, are also described; there are 14 of them altogether. All of the exceptional Lie superalgebras are obtained with the help of the Cartan prolongation or a generalized prolongation.
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Bibliographic Information
  • Irina Shchepochkina
  • Affiliation: On leave of absence from the Independent University of Moscow; Correspondence: c/o D. Leites, Department of Mathematics, University of Stockholm, Roslagsv. 101, Kräftriket hus 6, S-106 91, Stockholm, Sweden
  • Email:,
  • Published electronically: October 13, 1999
  • Additional Notes: I am thankful to D. Leites for raising the problem and help; to INTAS grant 96-0538 and NFR for financial support; University of Twente and Stockholm University for hospitality. Computer experiments by G. Post and P. Grozman encouraged me to carry on with unbearable calculations.
  • © Copyright 1999 American Mathematical Society
  • Journal: Represent. Theory 3 (1999), 373-415
  • MSC (1991): Primary 17A70; Secondary 17B35
  • DOI:
  • MathSciNet review: 1715110