Abstract

The purpose of this paper is to obtain some inequalities and certain bounds for the dimension of the c-nilpotent multiplier of finite dimensional nilpotent Lie algebras and their factor Lie algebras. Also, we give an inequality for the dimension of the c-nilpotent multiplier of L connected with dimension of the Lie algebras γd (L) and L / Zd−1 (L) . Finally, we compare our results with the previously known result.

Highlights

  • All Lie algebras referred to in this article are over a fixed field F and the square brackets [, ] denotes the Lie product

  • Let 0→R→F→L→0 be a free presentation of a Lie algebra L, where F is a free Lie algebra

  • We show that for each ideal N in L, there is a close relationship between the M(c) (L) and M(c) (L / N)

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Summary

Introduction

All Lie algebras referred to in this article are (of finite or infinite dimension) over a fixed field F and the square brackets [ , ] denotes the Lie product. Let L be Lie algebra with a free presentation 0→R→F→L→0. The following corollary is an immediate consequence of Lemma 1.1, which gives some elementary results about dimension of the c-nilpotent multiplier of finite dimensional Lie algebras see corollary 2.2 of Salemkar et al [6]. Let F be a free Lie algebra generated by n elements and L ≅ F / R Witt,s formula from Bahturin et al [7] gives us d

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