On the dimension of the product [L2,L2,L1]‎ in free Lie algebras

Document Type : Ischia Group Theory 2016

Author

Ahi Evran University

Abstract

Let L be a free Lie algebra of rank r2 over a field F and let Ln denote the degree n homogeneous component of L‎. ‎By using the dimensions of the corresponding homogeneous and fine homogeneous components of the second derived ideal of free centre-by-metabelian Lie algebra over a field F‎, ‎we determine the dimension of [L2,L2,L1]‎. ‎Moreover‎, ‎by this method‎, ‎we show that the dimension of [L2,L2,L1] over a field of characteristic 2 is different from the dimension over a field of characteristic other than 2.

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Volume 7, Issue 2 - Serial Number 2
Proceedings of the Ischia Group Theory 2016-Part II
June 2018
Pages 45-50
  • Receive Date: 21 November 2016
  • Revise Date: 05 April 2017
  • Accept Date: 25 March 2017
  • Published Online: 01 June 2018