Nonassociative rings and algebras Lie algebras: basic notions Concept
Hall basis
Summary
A Hall basis is a basis of a free Lie algebra made of iterated brackets of the generators. The brackets are chosen by a Hall set. This is a totally ordered set of binary trees with simple rules on how a tree splits into its two subtrees. Hall bases give explicit bases of free Lie algebras, and the related basic commutators describe the quotients of the lower central series of free groups. The Lyndon basis is one important Hall basis.
Further reading
About this page
| Tag | R1VQ49E4JA |
|---|---|
| URI | m2://R1VQ49E4JA |
| Kind | concept |
| Writing | W0 stub |
| MSC | 17B01, 17A50, 68R15 |
| Changed | 3 November 2026 |
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