Cohomologies of finite-dimensional simple alternative superalgebras of characteristic 3

The second cohomology groups for certain simple finite-dimensional alternative superalgebras of characteristic 3 are calculated, with coefficients in regular superbimodules. Contrary to the case of algebras, the groups are not trivial since the Wedderburn splitting theorem is not always true for alternative superalgebras. The results complement the similar results by N. A. Pisarenko for the case of characteristic not equal 2,3. (C) 2000 Academic Press.