由余张量余拟Hopf代数产生的拟量子群
Quasi-quantum groups arising from cotensor coquasi-Hopf algebras
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中文总结 AI 辅助
本文证明余张量余代数具有分次余拟Hopf结构，并建立其与余拟三角、余ribbon性质的保持及嵌入态射，同时证明余拟对映体的双射性并构造分次拟余拟Hopf配对。
中文摘要 AI 辅助
本文证明，对于任意余拟Hopf代数$H$和任意$H$-Majid双模$M$，余张量余代数$\operatorname{CoT}_H(M)$具有分次余拟Hopf代数结构。随后我们定义了余拟Hopf代数的标准滤过，并证明其相伴分次余拟Hopf代数可嵌入到保持零次和一次次的余张量余拟Hopf代数中。此外，若该余拟Hopf代数是余拟三角（相应地，余ribbon）的，则余张量余拟Hopf代数也是余拟三角（相应地，余ribbon）的，且上述嵌入是余拟三角（相应地，余ribbon）余拟Hopf代数的态射。作为副产品，我们证明了具有对偶Chevalley性质的余拟Hopf代数的余拟对映体是双射的。此外，我们建立了张量拟Hopf代数与余张量余拟Hopf代数之间的分次拟余拟Hopf配对。
英文摘要
In this paper, we show that for any coquasi-Hopf algebra $H$ and any $H$-Majid bimodule $M$, the cotensor coalgebra $\operatorname{CoT}_H(M)$ admits a graded coquasi-Hopf algebra structure. We then define the standard filtration of a coquasi-Hopf algebra and show that the associated graded coquasi-Hopf algebra admits an embedding into a cotensor coquasi-Hopf algebra that preserves degrees zero and one. If, in addition, this coquasi-Hopf algebra is coquasitriangular (respectively, coribbon), then the cotensor coquasi-Hopf algebra is also coquasitriangular (respectively, coribbon), and the above embedding is a morphism of coquasitriangular (respectively, coribbon) coquasi-Hopf algebras. As a byproduct, we prove that the coquasi-antipode of a coquasi-Hopf algebra with the dual Chevalley property is bijective. Moreover, we establish graded quasi-coquasi-Hopf pairings between tensor quasi-Hopf algebras and cotensor coquasi-Hopf algebras.
发表机构
- University of Science and Technology of China（中国科学技术大学）
- Nanjing University（南京大学）
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