The Schreier technique for subalgebras of a free Lie aegebra

Shmuel Rosset, Alon Wasserman

Research output: Contribution to journalArticlepeer-review

Abstract

In group theory Schreier's technique provides a basis for a subgroup of a tree 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.

Original languageEnglish
Pages (from-to)600-616
Number of pages17
JournalCanadian Journal of Mathematics
Volume49
Issue number3
DOIs
StatePublished - Jun 1997

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