This article is cited in 14 papers

Differential algebras and simple Jordan superalgebras

V. N. Zhelyabin<sup>ab

a</sup> Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk, Russia
^b Novosibirsk State University, Novosibirsk, Russia

Abstract: 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.

Key words: Jordan superalgebra, $(-1,1)$-superalgebra, superalgebra of vector type, differentially simple algebra, algebra of polynomials, projective module.

UDC: 512.554

Received: 14.09.2009

 English version: Siberian Advances in Mathematics, 2010, 20:3, 223–230

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