Agradecimentos: The author is grateful to Prof. Alexandre Pozhidaev (Sobolev Institute of Math., Russia) and Prof. Ivan Kaygorodov (UFABC, Brazil) for interest and constructive comments

Abstract: 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...

Abstract: 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 and and prove the Kronecker factorization theorem for superalgebras . In the last section we use a new approach to study noncommutative Jordan representations of simple Jordan superalgebras

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