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The Schreier Technique for Subalgebras of a Free Lie Algebra

Published online by Cambridge University Press:  20 November 2018

Shmuel Rosset  and
Alon Wasserman
Shmuel Rosset
Affiliation:
Tel-Aviv University, Ramat-Aviv 69978, Israel, e-mail: rosset@math.tau.ac.il, alonwa@math.tau.ac.il
Alon Wasserman
Affiliation:
Tel-Aviv University, Ramat-Aviv 69978, Israel, e-mail: rosset@math.tau.ac.il, alonwa@math.tau.ac.il
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Abstract

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In group theory Schreier's technique provides a basis for a subgroup of a free group. In this paper an analogue is developed for free Lie algebras. It hinges on the idea of cutting a Hall set into two parts. Using it, we show that proper subalgebras of finite codimension are not finitely generated and, following M. Hall, that a finitely generated subalgebra is a free factor of a subalgebra of finite codimension.

Keywords

17B01
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 49 , Issue 3 , 01 June 1997 , pp. 600 - 616
Copyright
Copyright © Canadian Mathematical Society 1997

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