This article is cited in
18 papers
Simple Special Jordan Superalgebras with Associative Nil-Semisimple Even Part
V. N. Zhelyabin Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences
Abstract:
We describe unital simple special Jordan superalgebras with associative nil-semisimple even part. In every such superalgebra
$J=A+M$, either
$M$ is an associative and commutative
$A$-module, or the associator space
$(A,A,M)$ coincides with
$M$. In the former case, if
$J$ is not a superalgebra of the non-degenerate bilinear superform then its even part
$A$ is a differentiably simple algebra and its odd part
$M$ is a finitely generated projective
$A$-module of rank 1. Multiplication in
$M$ is defined by fixed finite sets of derivations and elements of
$A$. If, in addition,
$M$ is one-generated then the initial superalgebra is a twisted superalgebra of vector type. The condition of being one-generated for
$M$ is satisfied, for instance, if
$A$ is local or isomorphic to a polynomial algebra. We also give a description of superalgebras for which
$(A,A,M)\neq 0$ and
$M\cap [A,M]\ne0$, where
$[\, ,\,]$ is a commutator in the associative enveloping superalgebra of
$J$. It is shown that such each infinite-dimensional superalgebra may be obtained from a simple Jordan superalgebra whose odd part is an associative module over the even.
Keywords:
unital simple special Jordan superalgebra, differentiably simple algebra, projective $A$-module.
UDC:
512.554 Received: 22.05.2000
Fulltext:
PDF file (2856 kB)
