Wedderburn principal theorem for Jordan superalgebras I

Abstract

We consider finite dimensional Jordan superalgebras J over an algebraically closed field of characteristic 0, with solvable radical N such that N=20 and J/N is a simple Jordan superalgebra of one of the following types: Kac K10, Kaplansky K3, superform or Dt.We prove that an analogue of the Wedderburn Principal Theorem (WPT) holds if certain restrictions on the types of irreducible subbimodules of N are imposed, where N is considered as a J/N-bimodule. Using counterexamples, it is shown that the imposed restrictions are essential.