辫子Hopf代数的积分(英)

Integrals of Braided Hopf Algebras

中文关键词:  积分  辫子Hopf代数.

英文关键词:integral  braided Hopf algebra.

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.