Differential algebras and simple Jordan superalgebras

In [14], a new example is constructed of a unital simple special Jordan superalgebra J over the field of reals. It turns out that J is a subsuperalgebra of a Jordan superalgebra of vector type but it cannot be isomorphic to a superalgebra of such a type. Moreover, the superalgebra of fractions of J is isomorphic to a Jordan superalgebra of vector type. In the present article, we find a similar example of a Jordan superalgebra. It is constructed over a field of characteristic 0 in which the equation t 2 + 1 = 0 has no solutions.