THE EQUATION [x,u]+[y,v]=0 IN FREE LIE ALGEBRAS

Remeslennikov, Vladimir and Stöhr, Ralph (2007) THE EQUATION [x,u]+[y,v]=0 IN FREE LIE ALGEBRAS. Internat. J. Algebra Comput., 17 (no. 5/). pp. 1165-1187. ISSN 1749-9097

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Abstract

We investigate equations of the form [x,u]+[y,v]=0 over a free Lie algebra L. In the case where u and v are free generators of L, we exhibit two series of solutions, we work out the dimensions of the homogeneous components of the solution space, and we determine its radical. In the general case we show that the results on free generator coefficients are sufficient to obtain the solution space up to finite codimension. As an application we determine the radical of the bilinear equation [x_1,x_2]+[x_3,x_4]=0.

Item Type:	Article
Uncontrolled Keywords:	Equations, Free Lie Algebras
Subjects:	MSC 2010, the AMS's Mathematics Subject Classification > 17 Nonassociative rings and algebras
Depositing User:	Prof Ralph Stöhr
Date Deposited:	13 Dec 2007
Last Modified:	20 Oct 2017 14:12
URI:	https://eprints.maths.manchester.ac.uk/id/eprint/994

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