Systems of linear equations and the word problem for the varieties \({\mathfrak N}_2{\mathfrak N}_c\) of Lie algebras
type: Item
instance of: scholarly article
title: Systems of linear equations and the word problem for the varieties \({\mathfrak N}_2{\mathfrak N}_c\) of Lie algebras
zbMATH Open document ID: 0924.17003
author: L. K. Bektursynova
author: Ualbai Umirbaev
published in: Siberian Mathematical Journal
publication date: 1999-10-28T00:00:00Z
review text: Let \({\mathfrak N}_c\) be the variety of nilpotent Lie algebras of nilpotent class at most \(c+1\). The word problem for the varieties of polynilpotent Lie algebras \({\mathfrak N}_{c_1}{\mathfrak N}_{c_2}\cdots{\mathfrak N}_{c_k}\) was studied by many mathematicians. But the question of decidability for the word problem remained open for the varieties \({\mathfrak N}_2{\mathfrak N}_c\). Theorem 1. The word problem is decidable in the variety of Lie algebras \({\mathfrak N}_2{\mathfrak N}_c\). Corollary. The word problem is decidable in a variety \({\mathfrak M}\) of polynilpotent Lie algebras if and only if \({\mathfrak N}_3{\mathfrak N}_1\not\subseteq{\mathfrak M}\).
Mathematics Subject Classification ID: 17B01
Mathematics Subject Classification ID: 17B30
zbMATH DE Number: 1353840
zbMATH Keywords: variety of nilpotent Lie algebras
zbMATH Keywords: word problem
zbMATH Keywords: polynilpotent Lie algebras
zbMATH Keywords: decidability
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1353840