Representations of simple noncommutative Jordan superalgebras I

In this article we begin the study of representations of simple finite-dimensional noncommutative Jordan superalgebras. In the case of degree >= 3 we show that any finite-dimensional representation is completely reducible and, depending on the superalgebra, quasiassociative or Jordan. Then we study representations of superalgebras D-t (alpha, beta, gamma) and K-3 (alpha, beta, gamma) and prove the Kronecker factorization theorem for superalgebras D-t (alpha, beta, gamma). In the last section we use a new approach to study noncommutative Jordan representations of simple Jordan superalgebras. (C) 2019 Elsevier Inc. All rights reserved.