Algebra & Number Theory
- Algebra Number Theory
- Volume 8, Number 5 (2014), 1179-1199.
Cosemisimple Hopf algebras are faithfully flat over Hopf subalgebras
The question of whether or not a Hopf algebra is faithfully flat over a Hopf subalgebra has received positive answers in several particular cases: when (or more generally, just ) is commutative, cocommutative, or pointed, or when contains the coradical of . 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” is always a cosemisimple coalgebra, and that the expectation is positive when is a CQG algebra.
Algebra Number Theory, Volume 8, Number 5 (2014), 1179-1199.
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
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
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]
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