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Pure Mathematics 2025
ω-Dendriform代数和ω-Quadri代数
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Abstract:
本文定义了ω-dendriform代数和ω-quadri代数，并且研究了他们之间的代数结构的关系。首先，引入ω-左对称代数的表示的定义，研究其与ω-李代数的表示之间的关系。然后，类比结合代数与dendriform代数和quadri代数之间的关系，定义ω-dendriform代数和ω-quadri代数，并且研究了ω-李代数、ω-左对称代数、ω-dendriform代数和ω-quadri代数之间的关系。
In this paper, we define ω-dendriform algebra and ω-quadri algebra, and study the relationship between them. Firstly, the definition of representation of ω-left-symmetric algebra is introduced, and the relationship between the representation on ω-dendriform algebra and ω-Lie algebra is studied. Then, by analogying the relationship among associative algebra, dendriform algebra and quadri algebra, ω-dendriform algebra and ω-quadri algebra are defined, and the relationship among ω-Lie algebra, ω-left-symmetric algebra, ω-dendriform algebra and ω-quadri algebra is studied.
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