Simple quotient algebras and subalgebras of Jacobian algebras
type: Item
instance of: scholarly article
title: Simple quotient algebras and subalgebras of Jacobian algebras
zbMATH Open document ID: 0936.17006
DOI: 10.1007/BF02673908
published in: Siberian Mathematical Journal
publication date: 2000-04-16T00:00:00Z
review text: A Jacobian algebra is an \(n\)-Lie algebra with an \(n\)-ary multiplication operation defined by means of a certain Jacobian. Answering the question posed by \textit{V. T. Filippov} in [Sib. Math. J. 39, No. 3, 573-581 (1998; Zbl 0936.17005)], the author proves that, for certain subalgebras of Jacobian algebras, the quotient algebras by centers are simple. In particular, the first examples are constructed of simple finite-dimensional \(n\)-Lie algebras over a field of characteristic \(p>0\), namely, of dimensions \(p^n-1,\;p^n-2,\;p^{n-1}\), and \(p^{n-1}-1\).
Mathematics Subject Classification ID: 17A42
Mathematics Subject Classification ID: 17B60
zbMATH DE Number: 1432400
zbMATH Keywords: simple \(n\)-Lie algebra
zbMATH Keywords: Jacobian algebras
author: Alexandre P. Pojidaev
reviewed by: Ivan Shestakov
MaRDI profile type: Publication
cites work: Q3710656
cites work: On an \(n\)-Lie algebra of Jacobians
Recommended article: Simple subalgebras of special simple Jordan algebras
Recommended article: Algebras of quotients of Jordan algebras
Recommended article: Algebras of quotients of nonsingular Jordan algebras
Recommended article: Algebras of Quotients of Jordan–Lie Algebras
Recommended article: Q3825126
Recommended article: Q3646854
Recommended article: SUBALGEBRAS OF THE POLYNOMIAL ALGEBRA IN POSITIVE CHARACTERISTIC AND THE JACOBIAN
Recommended article: Quasivariety of special Jordan algebras
Recommended article: Jacobi quasi-Nijenhuis algebroids
Recommended article: Q3698972
description: scientific article; zbMATH DE number 1432400