On linear equations in free Lie algebras

Alaa Altassan, Ralph Stöhr

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    We investigate equations of the form [x1, u1]+,...,+[xk, uk]=0 over a free Lie algebra L. In the case where the coefficients u1,..., uk 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. © 2011 Elsevier Inc.
    Original languageEnglish
    Pages (from-to)329-341
    Number of pages12
    JournalJournal of Algebra
    Issue number1
    Publication statusPublished - 1 Jan 2012


    • Equations
    • Free Lie algebras


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