New Examples of Simple Jordan Superalgebras over an Arbitrary Field of Characteristic Zero

摘要

I.P. Shestakov constructed an example of a unital simple special Jordansuperalgebra over the field of real numbers. It turned out to be asubsuperalgebra of the Jordan superalgebra of vector type, but not isomorphicto a superalgebra of this type. Moreover, its superalgebra of fractions isisomorphic to a Jordan superalgebra of vector type. Author constructed asimilar example of a Jordan superalgebra over a field of characteristic~0 inwhich the equation $t^2+1=0$. In this article we present an~example of a Jordansuperalgebra with the same properties over an arbitrary field of characteristic0. A similar example of a superalgebra is found in the Cheng-Kac superalgebra.