The Cartan-type modular Lie superalgebra KO

The finite-dimensional odd contact Lie superalgebras KO(n, n + 1, t) over a field of prime characteristic are studied, where n is a positive integer and t is an n-tuple of non-negative integers. In particular, it is proven that KO(n, n + 1, t) is simple and has no non-singular associative bilinear forms. Moreover, an explicit description of the derivation superalgebra of KO(n, n + 1, t) is given, and as a consequence it is shown that the outer derivation superalgebra of KO(n, n + 1, t) is Abelian of dimension Sigma(n)(i=1) t(i) - n.