Bulletin of the Belgian Mathematical Society - Simon Stevin

Split extension classifiers in the category of cocommutative Hopf algebras

Marino Gran, Gabriel Kadjo, and Joost Vercruysse

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Abstract

We describe the split extension classifiers in the semi-abelian category of cocommutative Hopf algebras over an algebraically closed field of characteristic zero. The categorical notions of centralizer and of center in the category of cocommutative Hopf algebras is then explored. We show that the categorical notion of center coincides with the one that is considered in the theory of general Hopf algebras.

Article information

Source
Bull. Belg. Math. Soc. Simon Stevin, Volume 25, Number 3 (2018), 355-382.

Dates
First available in Project Euclid: 11 September 2018

Permanent link to this document
https://projecteuclid.org/euclid.bbms/1536631232

Digital Object Identifier
doi:10.36045/bbms/1536631232

Mathematical Reviews number (MathSciNet)
MR3852673

Zentralblatt MATH identifier
06970019

Subjects
Primary: 16S40: Smash products of general Hopf actions [See also 16T05] 16T05: Hopf algebras and their applications [See also 16S40, 57T05] 16U70: Center, normalizer (invariant elements) 18E10: Exact categories, abelian categories 20J99: None of the above, but in this section

Keywords
cocommutative Hopf algebra split extension classifier, universal object centralizer center

Citation

Gran, Marino; Kadjo, Gabriel; Vercruysse, Joost. Split extension classifiers in the category of cocommutative Hopf algebras. Bull. Belg. Math. Soc. Simon Stevin 25 (2018), no. 3, 355--382. doi:10.36045/bbms/1536631232. https://projecteuclid.org/euclid.bbms/1536631232


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