FINITE-DIMENSIONAL SPECIAL ODD HAMILTONIAN SUPERALGEBRAS IN PRIME CHARACTERISTIC

Abstract

In this paper, we study a new family of finite-dimensional simple Lie superalgebras of Cartan type over a field of characteristic p > 3, the so-called special odd Hamiltonian superalgebras. The spanning sets are first given and then the grading structures are described explicitly. Finally, the simplicity and the dimension formulas are determined. As application, using the dimension formulas, we make a comparison between the special odd Hamiltonian superalgebras and the other known families of finite-dimensional simple modular Lie superalgebras of Cartan type.