Taiwanese Journal of Mathematics

BICOVARIANT DIFFERENTIAL CALCULI ON A WEAK HOPF ALGEBRA

Haixing Zhu, Shuanhong Wang, and Juzhen Chen

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Abstract

Let $H$ be a weak Hopf algebra with bijective antipode. In this paper we follow Woronowicz's fundamental method to characterize bicovariant differential calculi on $H$. We show that there exists a 1-1 correspondence between bicovariant differential calculi and some right ideals of $H$ contained in $ ker \varepsilon_s $ such that these ideals are right $H$-comodules with coadjoint maps, where $\varepsilon_s$ is the source map of $H$. This is a generalization of well-known Woronowicz's theorem about bicovariant differential calculi on quantum groups.

Article information

Source
Taiwanese J. Math., Volume 18, Number 6 (2014), 1679-1712.

Dates
First available in Project Euclid: 21 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1500667491

Digital Object Identifier
doi:10.11650/tjm.18.2014.4046

Mathematical Reviews number (MathSciNet)
MR3284026

Zentralblatt MATH identifier
1357.16052

Subjects
Primary: 16T05: Hopf algebras and their applications [See also 16S40, 57T05] 57T05: Hopf algebras [See also 16T05]

Keywords
weak Hopf algebra quantum groupoid bicovariant differential calculus

Citation

Zhu, Haixing; Wang, Shuanhong; Chen, Juzhen. BICOVARIANT DIFFERENTIAL CALCULI ON A WEAK HOPF ALGEBRA. Taiwanese J. Math. 18 (2014), no. 6, 1679--1712. doi:10.11650/tjm.18.2014.4046. https://projecteuclid.org/euclid.twjm/1500667491


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