Integrals of Braided Hopf Algebras

Abstract

The faithful quasi-dual $H^d$ and strict quasi-dual $H^{d^{\prime }}$ of an infinite braided Hopf algebra $H$ are introduced and it is proved that every strict quasi-dual $H^{d^{\prime }}$ is an $H$-Hopf module. The connection between the integrals and the maximal rational $H^d$-submodule $H^{drat}$ of $H^d$ is found. That is, $H^{drat}\cong {\int }_{H^d}^l\otimes H$ is proved. The existence and uniqueness of integrals for braided Hopf algebras in the Yetter-Drinfeld category ${(}_B^B\mathcal{YD},C)$ are given.

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References in corpus (2)

• Classical Yang-Baxter Equation and Low Dimensional Triangular Lie Bialgebras
• The Radicals of Hopf Module Algebras

Cited by in corpus (1)

• On braided co-Frobenius Hopf algebras