Finite dimensional special odd contact superalgebras over a field of prime characteristic

Abstract

This paper considers a family of finite dimensional simple Lie superalgebras of Cartan type over a field of characteristic $p>3$, the so-called special odd contact superalgebras. First, the spanning sets are determined for the Lie superalgebras and their relatives. Second, the spanning sets are used to characterize the simplicity and to compute the dimension formulas. Third, we determine the superderivation algebras and the first cohomology groups. Finally, the dimension formulas and the first cohomology groups are used to make a comparison between the special odd contact superalgebras and the other simple Lie superalgebras of Cartan type.