Monomial bases and pre-Lie structure for free Lie algebras
Mahdi J. Hasan Al-Kaabi, Dominique Manchon, Fr\'ed\'eric Patras
TL;DR
This paper introduces a pre-Lie algebra structure on free Lie algebras, providing explicit presentations and describing Gr"obner bases using tree structures, advancing algebraic understanding.
Contribution
It constructs a pre-Lie structure on free Lie algebras and characterizes Gr"obner bases via trees, offering new algebraic tools and explicit presentations.
Findings
Pre-Lie structure on free Lie algebras constructed
Explicit presentation of free Lie algebra as quotient
Gr"obner bases described in terms of trees
Abstract
In this paper, we construct a pre-Lie structure on the free Lie algebra L(E) generated by a set E, giving an explicit presentation of L(E) as the quotient of the free pre-Lie algebra generated by E, by some ideal I. The main result in this paper is a description of Gr\"obner bases in terms of trees.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAdvanced Topics in Algebra · Algebraic structures and combinatorial models · Homotopy and Cohomology in Algebraic Topology