%0 Journal Article
%T <i>&#969;</i>-Dendriform代数和<i>&#969;</i>-Quadri代数<br><i>&#969;</i>-Dendriform Algebras and <i>&#969;</i>-Quadri Algebras
%A 王秋艳
%J Pure Mathematics
%P 114-128
%@ 2160-7605
%D 2025
%I Hans Publishing
%R 10.12677/pm.2025.152053
%X 本文定义了<i>&#969;</i>-dendriform代数和<i>&#969;</i>-quadri代数&#65292;并且研究了他们之间的代数结构的关系。首先&#65292;引入<i>&#969;</i>-左对称代数的表示的定义&#65292;研究其与<i>&#969;</i>-李代数的表示之间的关系。然后&#65292;类比结合代数与dendriform代数和quadri代数之间的关系&#65292;定义<i>&#969;</i>-dendriform代数和<i>&#969;</i>-quadri代数&#65292;并且研究了<i>&#969;</i>-李代数、<i>&#969;</i>-左对称代数、<i>&#969;</i>-dendriform代数和<i>&#969;</i>-quadri代数之间的关系。<br>In this paper, we define <i>&#969;</i>-dendriform algebra and <i>&#969;</i>-quadri algebra, and study the relationship between them. Firstly, the definition of representation of <i>&#969;</i>-left-symmetric algebra is introduced, and the relationship between the representation on <i>&#969;</i>-dendriform algebra and <i>&#969;</i>-Lie algebra is studied. Then, by analogying the relationship among associative algebra, dendriform algebra and quadri algebra, <i>&#969;</i>-dendriform algebra and <i>&#969;</i>-quadri algebra are defined, and the relationship among <i>&#969;</i>-Lie algebra, <i>&#969;</i>-left-symmetric algebra, <i>&#969;</i>-dendriform algebra and <i>&#969;</i>-quadri algebra is studied.
%K <i>&#969
%K </i>-李代数&#65292
%K <i>&#969
%K </i>-Dendriform代数&#65292
%K <i>&#969
%K </i>-Quadri代数<br><i>&#969
%K </i>-Lie Algebra
%K <i>&#969
%K </i>-Dendriform Algebra
%K <i>&#969
%K </i>-Quadri Algebra
%U http://www.hanspub.org/journal/PaperInformation.aspx?PaperID=108002