This article is cited in 23 papers

Simple special Jordan superalgebras with associative even part

V. N. Zhelyabin, I. P. Shestakov

Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences

Abstract: We describe the simple special unital Jordan superalgebras with associative even part $A$ whose odd part $M$ is an associative module over $A$. We prove that each of these superalgebras, not isomorphic to a superalgebra of nondegenerate bilinear superform, is isomorphically embedded into a twisted Jordan superalgebra of vector type. We exhibit a new example of a simple special Jordan superalgebra. We also describe the superalgebras such that $M\cap[A,M]\ne0$.

Keywords: Jordan superalgebra, $(-1,1)$-superalgebra, twisted superalgebra of vector type, differentiably simple algebra, projective module, localization of module.

UDC: 512.554

Received: 09.02.2004

 English version: Siberian Mathematical Journal, 2004, 45:5, 860–882

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