New Examples of Simple Jordan Superalgebras over an Arbitrary Field
of Characteristic Zero
I.P. Shestakov constructed an example of a unital simple special
Jordan superalgebra over the field of real numbers. It turned out to be a
subsuperalgebra of the Jordan superalgebra of vector type, but not
isomorphic to a superalgebra of this type. Moreover, its superalgebra of
fractions is isomorphic to a Jordan superalgebra of vector type. The author
constructed a similar example of a Jordan superalgebra over a field of
characteristic 0 in which the equation t2 + 1 = 0 has no solutions.
In this article we
present an example of a Jordan superalgebra with the same properties over
an arbitrary field of characteristic 0. A similar example of a
superalgebra is found in the Cheng-Kac superalgebra.
V.N. Zhelyabin < vicnic@math.nsc.ru >