Journal of Lie Theory

Let g be any finite-dimensional odd Contact superalgebra over a field of prime characteristic. By means of determining the minimal dimensions of image spaces of certain inner superderivations, it is proved that the principal filtration of g is invariant under the automorphisms of g. Then, the parameters by which g is defined are proved to be intrinsic and thereby the odd Contact superalgebras are classified up to isomorphisms. Furthermore, the restrictedness of g is determined and the automorphism group of g in restrictedness case is proved to be isomorphic to the admissible automorphism group of the underlying superalgebra of g under a concrete isomorphism Φ. Further properties of Φ are given and as an application, the results above are used to discuss the p-characters of the irreducible representations for g.