Simple finite-dimensional modular noncommutative Jordan superalgebras. (English) Zbl 1472.17003
Summary: We classify the central simple finite-dimensional noncommutative Jordan superalgebras over an algebraically closed field of characteristic \(p > 2\). The case of characteristic 0 was considered by the authors in the previous paper [Sib. Math. J. 54, No. 2, 301–316 (2013; Zbl 1276.17017); translation from Sib. Mat. Zh. 54, No. 2, 389–406 (2013)]. In particular, we describe Leibniz brackets on all finite dimensional central simple Jordan superalgebras except mixed (nor vector neither Poisson) Kantor doubles of the supercommutative superalgebra \(B(m, n)\).
MSC:
| 17A15 | Noncommutative Jordan algebras |
| 17A20 | Flexible algebras |
| 17B63 | Poisson algebras |
| 17C20 | Simple, semisimple Jordan algebras |
| 17C70 | Super structures |
Citations:
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