Jordan elements and Left-Center of a Free Leibniz algebra

Q3 Mathematics

Electronic Research Announcements in Mathematical Sciences Pub Date : 2011-07-01 DOI:10.3934/ERA.2011.18.31

A. Dzhumadil'daev

引用次数: 2

Abstract

An element of a free Leibniz algebra is called Jordan if it belongs to a free Leibniz-Jordan subalgebra. Elements of the Jordan commutant of a free Leibniz algebra are called weak Jordan. We prove that an element of a free Leibniz algebra over a field of characteristic 0 is weak Jordan if and only if it is left-central. We show that free Leibniz algebra is an extension of a free Lie algebra by left-center. We find the dimensions of the homogeneous components of the Jordan commutant and the base of its multilinear part. We find criterion for an element of free Leibniz algebra to be Jordan.

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自由莱布尼兹代数的Jordan元与左中心

如果一个自由莱布尼兹代数的元素属于一个自由莱布尼兹-乔丹子代数，则称它为乔丹。自由莱布尼兹代数的约当交换子的元素称为弱约当。证明特征为0的域上的自由莱布尼兹代数的一个元素是弱约当当且仅当它是左中心的。证明了自由莱布尼茨代数是自由李代数的左中心扩展。我们求出了Jordan交换子的齐次分量的维数及其多线性部分的底。我们找到了自由莱布尼兹代数的一个元素为Jordan的判据。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Electronic Research Announcements in Mathematical Sciences 数学-数学

CiteScore

0.90

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Electronic Research Archive (ERA), formerly known as Electronic Research Announcements in Mathematical Sciences, rapidly publishes original and expository full-length articles of significant advances in all branches of mathematics. All articles should be designed to communicate their contents to a broad mathematical audience and must meet high standards for mathematical content and clarity. After review and acceptance, articles enter production for immediate publication. ERA is the continuation of Electronic Research Announcements of the AMS published by the American Mathematical Society, 1995—2007