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MiS Preprint

Simple Lie superalgebras and non-integrable distributions in characteristic $p$

Sofiane Bouarroudj and Dimitry A. Leites


Recently, Grozman and Leites returned to the original Cartan's description of Lie algebras to interpret the Melikyan algebras (for $p\leq 5$) 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 the field of complex numbers; for $p=3$, we obtain a series of new simple Lie superalgebras and an exceptional one.

Aug 22, 2006
Aug 22, 2006
MSC Codes:
17B50, 70F25
simple Lie superalgebras, nonholonomic structures

Related publications

2006 Journal Open Access
Sofiane Bouarroudj and D. A. Leites

Simple Lie superalgebras and nonintegrable distributions in characteristic p

In: Zapiski naucnych seminarov POMI, 331 (2006) 14, 15-29, 221