## 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 - DOI: https://doi.org/10.1090/S1088-4165-99-00012-6
- Published electronically: October 13, 1999
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## Abstract:

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: mleites@matematik.su.se, lra@paramonova.mccme.ru
- 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: https://doi.org/10.1090/S1088-4165-99-00012-6
- MathSciNet review: 1715110