Basic Commutators in n-Lie Algebras
Farshid Saeedi, Seyedeh Nafiseh Akbarossadat
TL;DR
This paper explores the structure of free n-Lie algebras, introduces basic commutators, generalizes the Witt formula, and establishes a basis for the lower central series.
Contribution
It provides a detailed structure of free n-Lie algebras and extends the concept of basic commutators and the Witt formula to this setting.
Findings
Derived the structure of free n-Lie algebras
Introduced basic commutators in n-Lie algebras
Proved a basis for the lower central series
Abstract
In this paper, we give the structure of free n-Lie algebras. Next, we introduce basic commutators in n-Lie algebras and generalize the Witt formula to calculate the number of the basic commutators. Also, we prove that the set of all of the basic commutators of weight w and length n+(w-2)(n-1) is a basis for Fw, where Fw is the wth term of the lower central series in the free n-Lie algebra F.
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 · Finite Group Theory Research