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Zapiski Nauchnykh Seminarov POMI, 2006, Volume 331, Pages 15–29
(Mi znsl247)
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This article is cited in 22 scientific papers (total in 22 papers)
Simple Lie superalgebras and nonintegrable distributions in characteristic $p$
S. Bouarroudja, D. A. Leitesb a United Arab Emirates University
b Stockholm University
Abstract:
Recently, Grozman and Leites returned to the original Cartan's description of Lie algebras to interpret the Melikyan algebras (for $p\le 5$) and several other little-known simple Lie algebras
over algebraically closed fields for $p=3$ as subalgebras of Lie algebras of vector fields preserving nonintegrable distributions analogous to (or identical with) those preserved by $G(2)$, $O(7)$, $Sp(4)$, and $Sp(10)$. The description was performed in terms of Cartan–Tanaka–Shchepochkina prolongs using Shchepochkina's algorithm and with the help of SuperLie package. Grozman and Leites also found two new series of simple Lie algebras.
Here we apply the same method to distributions preserved by one of the two exceptional simple finite dimensional Lie superalgebras over $\mathbb C$; for $p=3$, we obtain a series of new simple Lie superalgebras and an exceptional one.
Received: 19.05.2006
Citation:
S. Bouarroudj, D. A. Leites, “Simple Lie superalgebras and nonintegrable distributions in characteristic $p$”, Representation theory, dynamical systems, combinatorial and algoritmic methods. Part XIV, Zap. Nauchn. Sem. POMI, 331, POMI, St. Petersburg, 2006, 15–29; J. Math. Sci. (N. Y.), 141:4 (2007), 1390–1398
Linking options:
https://www.mathnet.ru/eng/znsl247 https://www.mathnet.ru/eng/znsl/v331/p15
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Abstract page: | 393 | Full-text PDF : | 104 | References: | 62 |
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