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

2010/07/16 by V. N. Zhelyabin, Zhelyabin, V. N.
Mathematics · #17C70 #FOS: Mathematics #Rings and Algebras (math.RA) #math.RA #msc:17C70

paper · pdf · doi:10.48550/arxiv.1007.2772

arxiv created 2010/07/16 · arxiv updated 2010/07/19

Abstract

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. Author constructed a similar example of a Jordan superalgebra over a field of characteristic~0 in which the equation t²+1=0. 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.

Related

• Representations of simple Jordan superalgebras
• Simple decompositions of simple special Jordan superalgebras
• Maximal subalgebras of Jordan superalgebras
• Simple Jordan superalgebras with the even parts of Clifford type
• Ternary superderivations of Jordan superalgebras