Basic Commutators in n-Lie Algebras

2023/01/29 by Saeedi, Farshid, Akbarossadat, Seyedeh Nafiseh
Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Finite Group Theory Research #Rings and Algebras (math.RA)

paper · pdf · doi:10.48550/arxiv.2301.12427

openalex publication_date 2023/01/29 · openalex created_date 2023/02/02 · openalex updated_date 2026/07/28

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.

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