This article is cited in 6 papers

On the structure of free dual Leibniz algebras

A. Naurazbekova

Department of Mechanics and Mathematics, L.N. Gumilyov Eurasian National University, 2 Satpaev St, 010008 Nur-Sultan, Kazakhstan

Abstract: It is proved that over a field of characteristic zero the free dual Leibniz algebras are the free associative-commutative algebras (without unity) with respect to the multiplication $a\circ b = ab+ba$ and their free generators are found. We construct the examples of subalgebras of two-generated free dual Leibniz algebra, that are free dual Leibniz algebras of countable rank.

Keywords and phrases: free dual Leibniz algebra, left-normed word, Lyndon–Shirshov word.

MSC: 17A50, 17D99, 17A32

Received: 23.04.2018

Language: English

DOI: 10.32523/2077-9879-2019-10-3-40-47

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