Algebra & Number Theory

Cosemisimple Hopf algebras are faithfully flat over Hopf subalgebras

Alexandru Chirvasitu

Full-text: Open access

Abstract

The question of whether or not a Hopf algebra H is faithfully flat over a Hopf subalgebra A has received positive answers in several particular cases: when H (or more generally, just A) is commutative, cocommutative, or pointed, or when K contains the coradical of H. We prove the statement in the title, adding the class of cosemisimple Hopf algebras to those known to be faithfully flat over all Hopf subalgebras. We also show that the third term of the resulting “exact sequence” AHC is always a cosemisimple coalgebra, and that the expectation HA is positive when H is a CQG algebra.

Article information

Source
Algebra Number Theory, Volume 8, Number 5 (2014), 1179-1199.

Dates
Received: 11 August 2013
Revised: 6 March 2014
Accepted: 21 April 2014
First available in Project Euclid: 20 December 2017

Permanent link to this document
https://projecteuclid.org/euclid.ant/1513730228

Digital Object Identifier
doi:10.2140/ant.2014.8.1179

Mathematical Reviews number (MathSciNet)
MR3263140

Zentralblatt MATH identifier
1346.16026

Subjects
Primary: 16T20: Ring-theoretic aspects of quantum groups [See also 17B37, 20G42, 81R50]
Secondary: 16T15: Coalgebras and comodules; corings 16T05: Hopf algebras and their applications [See also 16S40, 57T05] 20G42: Quantum groups (quantized function algebras) and their representations [See also 16T20, 17B37, 81R50]

Keywords
cosemisimple Hopf algebra CQG algebra faithfully flat right coideal subalgebra quotient left module coalgebra expectation

Citation

Chirvasitu, Alexandru. Cosemisimple Hopf algebras are faithfully flat over Hopf subalgebras. Algebra Number Theory 8 (2014), no. 5, 1179--1199. doi:10.2140/ant.2014.8.1179. https://projecteuclid.org/euclid.ant/1513730228


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