This article is cited in 2 papers

Structure of some unital simple Jordan superalgebras with associative even part

V. N. Zhelyabin

Sobolev Institute of Mathematics, Novosibirsk, Russia

Abstract: Studying the unital simple Jordan superalgebras with associative even part, we describe the unital simple Jordan superalgebras such that every pair of even elements induces the zero derivation and every pair of two odd elements induces the zero derivation of the even part. We show that such a superalgebra is either a superalgebra of nondegenerate bilinear form over a field or a four-dimensional simple Jordan superalgebra.

Keywords: Jordan superalgebra, Grassmann superalgebra, superalgebra of bilinear form, derivation, associative commutative algebra, composition algebra, superalgebra of vector type, differential algebra, projective module.

UDC: 512.554

Received: 21.03.2018

DOI: 10.17377/smzh.2018.59.608

 English version: Siberian Mathematical Journal, 2018, 59:6, 1051–1062

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