Representations of simple noncommutative Jordan superalgebras II

Abstract

In this article we continue the study of representations of simple finite-dimensional noncommutative Jordan superalgebras. We prove that an irreducible unital bimodule over a simple noncommutative Jordan superalgebra U of degree ≥2 is either an irreducible bimodule over its symmetrized superalgebra U ( + ) or is equal to one of its Peirce components. Applying this result, we describe irreducible finite-dimensional representations of simple noncommutative Jordan superalgebras U ( V , f , ⋆ ) and K ( Γ n , A ) , completing the description of simple finite-dimensional unital bimodules over simple noncommutative Jordan superalgebras over an algebraically closed field of characteristic 0.