Termination for a class of algorithms for constructing algebras given by generators and relations
type: Item
instance of: scholarly article
title: Termination for a class of algorithms for constructing algebras given by generators and relations
zbMATH Open document ID: 0886.17001
DOI: 10.1016/S0022-4049(97)00021-2
author: Marc van Leeuwen
author: Marcel Roelofs
published in: Journal of Pure and Applied Algebra
publication date: 1998-04-26T00:00:00Z
review text: The article presents a class of algorithms which allows to create a multiplication table for a finitely-presented nonassociative (known to be finite-dimensional) algebra. The main example is a Lie algebra. The idea is to work in the free nonassociative algebra (instead of a free Lie algebra, for example) and to rewrite partial multiplication tables, using identities. The main assumption is that it is sufficient to verify identities on a linear basis. Under some assumptions the termination of the algorithms is guaranteed.
Mathematics Subject Classification ID: 17-08
Mathematics Subject Classification ID: 17A50
Mathematics Subject Classification ID: 17B01
Mathematics Subject Classification ID: 17A01
zbMATH DE Number: 1025706
zbMATH Keywords: free nonassociative algebra
zbMATH Keywords: free Lie algebra
zbMATH Keywords: structure constants
zbMATH Keywords: confluent rewrite system
zbMATH Keywords: algorithms
zbMATH Keywords: multiplication tables
zbMATH Keywords: identities
reviewed by: Victor Ufnarovski
describes a project that uses: LIESUPER
MaRDI profile type: Publication
cites work: Program for constructing a complete system of relations, basis elements, and commutator table for finitely presented Lie algebras and superalgebras
cites work: Lie algebra computations
cites work: An algorithm for the construction of matrix representations for finitely presented non-commutative algebras
cites work: Constructing matrix representations of finitely presented groups
cites work: On vector enumeration
cites work: Q4276364
full work available at URL: s0022-4049(97)00021-2
OpenAlex ID: W2102736167
description: scientific article; zbMATH DE number 1025706