Nonassociative algebras related to Hamiltonian operators in the formal calculus of variations
type: Item
instance of: scholarly article
title: Nonassociative algebras related to Hamiltonian operators in the formal calculus of variations
zbMATH Open document ID: 0847.17001
DOI: 10.1016/0022-4049(95)00062-2
author: J. Marshall Osborn
author: E. Zelmanov
published in: Journal of Pure and Applied Algebra
publication date: 1996-10-09T00:00:00Z
review text: An algebra is called Novikov if it satisfies the identities \((xy)z= (xz)y\) and \((x, y, z)= (y, x, z)\). Let \(A\) be a simple Novikov algebra over an algebraically closed field, and suppose \(A\) contains a maximal subalgebra \(H\) such that \(A/H\) has a finite-dimensional irreducible \(H\)-submodule. Such an algebra has a Weisfeiler filtration which leads to a graded algebra \(G\) associated with \(A\). The authors show that the algebra \(G\) has to be one of four types. Furthermore, the codimension of \(H\) is finite only for one of these types, and in this case it is 1. For \(A^*\) the closure of \(A\) with respect to the topology induced by the filtration, it is also shown that \(A^*= G^*\) for three of these types, assuming a certain added restriction for one of them.
Mathematics Subject Classification ID: 17A30
zbMATH DE Number: 802566
zbMATH Keywords: Novikov algebra
zbMATH Keywords: identities
zbMATH Keywords: simple Novikov algebra
zbMATH Keywords: Weisfeiler filtration
MaRDI profile type: Publication
full work available at URL: 0022-4049(95)00062-2
OpenAlex ID: W2051148512
cites work: Q3744927
cites work: Q3810799
cites work: Q3808269
cites work: ASYMPTOTIC BEHAVIOUR OF THE RESOLVENT OF STURM-LIOUVILLE EQUATIONS AND THE ALGEBRA OF THE KORTEWEG-DE VRIES EQUATIONS
cites work: Q4115555
cites work: Hamiltonian operators and algebraic structures related to them
cites work: Infinite dimensional primitive Lie algebras
cites work: SIMPLE IRREDUCIBLE GRADED LIE ALGEBRAS OF FINITE GROWTH
cites work: Equations of long waves with a free surface. II: Hamiltonian structure and higher equations
cites work: The geometry of conservative systems of hydrodynamic type. The method of averaging for field-theoretical systems
cites work: Q4854348
cites work: Q3129431
cites work: Simple novikov algebras with an idempotent
cites work: Infinite-dimensional filtered Lie algebras and their connection with graded Lie algebras
cites work: Q3765944
description: scientific article; zbMATH DE number 802566