On linear equations in free Lie algebras

JOURNAL OF ALGEBRA

卷:349

Article

Altassan, Alaa¹  Stoehr, Ralph¹ 

[1] Univ Manchester, Sch Math, Manchester M13 9PL, Lancs, England

关键词: Free Lie algebras;    Equations;   

DOI  :  10.1016/j.jalgebra.2011.10.012

来源: Elsevier

【 摘 要 】

We investigate equations of the form [x(1), u(1)]+ ... + [x(k), u(k)] = 0 over a free Lie algebra L. In the case where the coefficients u(1),..., 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. (C) 2011 Elsevier Inc. All rights reserved.

【 授权许可】

Free