Simple finite-dimensional noncommutative Jordan superalgebras of characteristic 0 (Q350854)

The \textit{degree} of a noncommutative Jordan superalgebra \(U\) over a field \(F\) is the maximum number of nonzero orthogonal idempotents in the scalar extension \({\overline F} \otimes_F U\), where \(\overline F\) is the algebraic closure of \(F\). In [Algebra Logic 49, No. 1, 18--42 (2010); translation from Algebra Logika 49, No. 1, 26--59 (2010; Zbl 1195.17025)], the authors classified central simple finite-dimensional noncommutative Jordan superalgebras of degree \(n > 2\) over a field of characteristic zero. In the present paper they complete this classification considering the remaining cases of degree \(1\) and \(2\). In the case of degree \(1\), the problem is reduced to the description of derivations of the Grassmann superalgebra with respect to which it is differentiably simple.