Infinite-dimensional modular special odd contact superalgebras

The infinite-dimensional special odd contact Lie superalgebras SKO(n,n+1;c) over a field of positive characteristic are studied. In particular, we prove that Lie superalgebras SKO(n,n+1;c) are simple. Besides, the Weisfeiler filtration of SKO(n,n+1;c) is proved to be invariant under automorphisms by characterizing -nilpotent elements. Thereby, we obtain some properties of these Lie superalgebras.