Recently, Grozman and Leites returned to the original Cartan's description of
Lie algebras to interpret the Melikyan algebras (for p<7) 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 C; for p=3, we
obtain a series of new simple Lie superalgebras and an exceptional one.Comment: 10 pages; no figure