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The Schreier technique for subalgebras of a free Lie algebra

  Published:1997-06-01
 Printed: Jun 1997
  • Shmuel Rosset
  • Alon Wasserman
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Abstract

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.
 

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