Integrals of Braided Hopf Algebras
Received:March 17, 2004  
Key Words: integral   braided Hopf algebra.  
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Author NameAffiliation
GUO Xi-jing Dept. of Math., Zhuhai Campus of Jilin University, Guangdong 519047, China 
ZHANG Shou-chuan$ Dept. of Math., Hunan University, Changsha 410082, China 
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      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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