The Wedderburn decomposition in finite-dimensional alternative superaigebras of characteristic 3

Abstract

The Wedderburn decomposition in finite dimensional alternative superaigebras of characteristic 3 is studied. It is proved that the decomposition exists provided the semisimple quotient superalgebra does not contain certain simple superaigebras. Counterexamples are given which show that the restrictions cannot be omitted. Together with the similar results by N.A.Pisarenko for the characteristic ≠ 2,3 case, the results of the paper give a description of Wedderburn decomposition for alternative superaigebras of characteristic ≠ 2.