New examples of simple Jordan superalgebras over an arbitrary field of characteristic 0

Zhelyabin, V.

doi:10.1090/S1061-0022-2013-01255-6

New examples of simple Jordan superalgebras over an arbitrary field of characteristic 0
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by V. N. Zhelyabin
Translated by: N. B. Lebedinskaya

St. Petersburg Math. J. 24 (2013), 591-600

DOI: https://doi.org/10.1090/S1061-0022-2013-01255-6

Published electronically: May 24, 2013

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Abstract:

In a joint paper with the author, I. P. Shestakov constructed a new example of a unital simple special Jordan superalgebra over the real number field. It turned out that this superalgebra is a subsuperalgebra of a Jordan superalgebra of the vector type $J(\Gamma ,D)$, but it is not isomorphic to a superalgebra of this type. Moreover, the superalgebra of quotients of the constructed superalgebra is isomorphic to a Jordan superalgebra of vector type. Later, a similar example was constructed for Jordan superalgebras over a field of characteristic 0 in which the equation $t^2+1=0$ is unsolvable. In the present paper, an example is given for a Jordan superalgebra with the same properties over an arbitrary field of characteristic 0. A similar example was discovered also for a Cheng–Kac superalgebra.

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