On linear equations in free Lie algebras

Altassan, Alaa and Stöhr, Ralph (2012) On linear equations in free Lie algebras. Journal of Algebra, 349 (1). pp. 329-341. ISSN 0021-8693

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Abstract

We investigate equations of the form $[x_1,u_1]+\ldots+[x_k,u_k]=0$ over a free Lie algebra $L$. In the case where the coefficients $u_1,\ldots,u_k$ are free generators of $L$, we generalize a number of earlier results on equations with two variables to equations with an arbitrary number of indeterminates. Our main results refer to the case where the coefficients coincide with the free generators of $L$. We give a detailed description of the solution space and we obtain an explicit basis for its multilinear fine homogeneous component.

Item Type: Article
Uncontrolled Keywords: Free Lie algebras; equations
Subjects: MSC 2010, the AMS's Mathematics Subject Classification > 17 Nonassociative rings and algebras
Depositing User: Prof Ralph Stöhr
Date Deposited: 15 Jul 2011
Last Modified: 20 Oct 2017 14:12
URI: http://eprints.maths.manchester.ac.uk/id/eprint/1654

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