郭夕敬,张寿传.辫子Hopf代数的积分(英)[J].数学研究及应用,2006,26(4):649~658 |
辫子Hopf代数的积分(英) |
Integrals of Braided Hopf Algebras |
投稿时间:2004-03-17 |
DOI:10.3770/j.issn:1000-341X.2006.04.002 |
中文关键词: 积分 辫子Hopf代数. |
英文关键词:integral braided Hopf algebra. |
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中文摘要: |
本文引进了无限维辫子Hopf代数$H$的忠实拟对偶$H^d$和严格拟对偶$H^{d'}$.证明了每个严格拟对偶$H^{d'}$是一个$H$-Hopf 模. 发现了$H^{d}$的极大有理$H^{d}$-子模$H^{d {\rm rat} }$ 与积分的关系, 即: $H^{d {\rm rat}}\cong \int ^l_{H^d} \otimes H$.给出了在Yetter-Drinfeld范畴$(^B_B{\cal YD},C)$中的辫子Hopf代数的积分的存在性和唯一性. |
英文摘要: |
The faithful quasi-dual $H^d$ and strict quasi-dual $H^{d'}$ of an infinite braided Hopf algebra $H$ are introduced and it is proved that every strict quasi-dual $H^{d'}$ is an $H$-Hopf module. A connection between the integrals and the maximal rational $H^{d}$-submodule $H^{d {\rm rat} }$ of $H^{d}$ is found. That is, $H^{d{\rm rat} }\cong \int ^l_{H^d} \otimes H$ is proved. The existence and uniqueness of integrals for braided Hopf algebras in the Yetter-Drinfeld category $(^B_B{\cal YD},C )$ are given. |
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