Representation Theory

ISSN 1088-4165



The five exceptional simple Lie
superalgebras of vector fields
and their fourteen regradings

Author: Irina Shchepochkina
Journal: Represent. Theory 3 (1999), 373-415
MSC (1991): Primary 17A70; Secondary 17B35
Published electronically: October 13, 1999
MathSciNet review: 1715110
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Abstract: The five simple exceptional complex Lie superalgebras of vector fields are described. One of them, ${\mathfrak{k}}{\mathfrak{as}}$, 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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Additional 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:, lra@paramonova,

Keywords: Lie superalgebra, Cartan prolongation, spinor representation
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.
Article copyright: © Copyright 1999 American Mathematical Society