Scholarlink

Abstract <p> An algebra with the identities <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11006_2025_3057_Article_IEq1.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="171" /> </InlineMediaObject> <EquationSource Format="TEX">\([a,b]c=2a(bc)-2b(ac)\)</EquationSource> </InlineEquation> and <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11006_2025_3057_Article_IEq2.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="174" /> </InlineMediaObject> <EquationSource Format="TEX">\(a[b,c]=2(ab)c-2(ac)b\)</EquationSource> </InlineEquation> is called a weak Leibniz algebra. It is shown that any weak Leibniz operad is self-dual and not Koszul. It is also proved that the polarization of any weak Leibniz algebra is a transposed Poisson algebra and vice versa, the depolarization of any transposed Poisson algebra is a weak Leibniz algebra. </p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Weak Leibniz Algebras

  • 期刊论文

  • 发表日期：

    2025年4月1日

查看全文
  • A. S. Dzhumadil’daev

摘要

Abstract

An algebra with the identities \([a,b]c=2a(bc)-2b(ac)\) and \(a[b,c]=2(ab)c-2(ac)b\) is called a weak Leibniz algebra. It is shown that any weak Leibniz operad is self-dual and not Koszul. It is also proved that the polarization of any weak Leibniz algebra is a transposed Poisson algebra and vice versa, the depolarization of any transposed Poisson algebra is a weak Leibniz algebra.