Basic Commutators in n-Lie Algebras

Farshid Saeedi; Seyedeh Nafiseh Akbarossadat

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arXiv · 2301.12427

Basic Commutators in n-Lie Algebras

Farshid Saeedi·Seyedeh Nafiseh Akbarossadat

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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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Farshid Saeedi, Seyedeh Nafiseh Akbarossadat. 2023-01-29. Basic Commutators in n-Lie Algebras. https://arxiv.org/abs/2301.12427

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