Jordan superalgebras with a solvable even part
type: Item
instance of: scholarly article
title: Jordan superalgebras with a solvable even part
zbMATH Open document ID: 0849.17035
DOI: 10.1007/BF00750553
published in: Algebra and Logic
publication date: 1996-11-14T00:00:00Z
review text: Let \(G= G_0 \oplus G_1\) be a Grassmann algebra over an associative commutative ring \(\Phi\). A \(\mathbb{Z}_2\)-graded \(\Phi\)-algebra \(J= J_0 \oplus J_1\) is said to be a Jordan superalgebra if the algebra \(G(J)= J_0 \otimes G_0 \otimes J_1 \otimes G_1\) is Jordan. The main result of the paper is the following criteria for solvability of Jordan superalgebras. Theorem A. Let \(J= J_0 \oplus J_1\) be a Jordan superalgebra over \(\Phi\), and \(1/6\in \Phi\). Then \(J\) is solvable if and only if the Jordan algebra \(J_0\) is solvable. First, the author proves an analogous statement for \(\mathbb{Z}_2\)-graded Jordan algebras \(J\). This proof is based upon clever computations in the multiplication algebra \(R(J)\). Then, Theorem A follows. As a consequence of this theorem the author obtains a criteria for solvability of color Jordan superalgebras.
Mathematics Subject Classification ID: 17C70
Mathematics Subject Classification ID: 17C10
zbMATH DE Number: 862294
zbMATH Keywords: Jordan superalgebra
zbMATH Keywords: solvability
zbMATH Keywords: color Jordan superalgebras
author: V. N. Zhelyabin
MaRDI profile type: Publication
cites work: Q4006527
cites work: Q3197984
description: scientific article; zbMATH DE number 862294