Geodesic
Differential algebras and simple Jordan superalgebras
Matematičeskie trudy, Tome 12 (2009) no. 2, pp. 41-51

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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. 
@article{MT_2009_12_2_a1,
     author = {V. N. Zhelyabin},
     title = {Differential algebras and simple {Jordan} superalgebras},
     journal = {Matemati\v{c}eskie trudy},
     pages = {41--51},
     publisher = {mathdoc},
     volume = {12},
     number = {2},
     year = {2009},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MT_2009_12_2_a1/}
}
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V. N. Zhelyabin. Differential algebras and simple Jordan superalgebras. Matematičeskie trudy, Tome 12 (2009) no. 2, pp. 41-51. http://geodesic.mathdoc.fr/item/MT_2009_12_2_a1/