Vol. 8, No. 5, 2014

Download this article
Download this article For screen
For printing
Recent Issues

Volume 10
Issue 9, 1845–2052
Issue 8, 1601–1843
Issue 7, 1373–1600
Issue 6, 1147–1371
Issue 5, 939–1146
Issue 4, 695–938
Issue 3, 451–694
Issue 2, 215–450
Issue 1, 1–214

Volume 9, 10 issues

Volume 8, 10 issues

Volume 7, 10 issues

Volume 6, 8 issues

Volume 5, 8 issues

Volume 4, 8 issues

Volume 3, 8 issues

Volume 2, 8 issues

Volume 1, 4 issues

The Journal
Cover
Editorial Board
Editors' Addresses
Editors' Interests
About the Journal
Scientific Advantages
Submission Guidelines
Submission Form
Subscriptions
Editorial Login
Contacts
Author Index
To Appear
 
ISSN: 1944-7833 (e-only)
ISSN: 1937-0652 (print)
Cosemisimple Hopf algebras are faithfully flat over Hopf subalgebras

Alexandru Chirvasitu

Vol. 8 (2014), No. 5, 1179–1199
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” A H C is always a cosemisimple coalgebra, and that the expectation H A is positive when H is a CQG algebra.

Keywords
cosemisimple Hopf algebra, CQG algebra, faithfully flat, right coideal subalgebra, quotient left module coalgebra, expectation
Mathematical Subject Classification 2010
Primary: 16T20
Secondary: 16T15, 16T05, 20G42
Milestones
Received: 11 August 2013
Revised: 6 March 2014
Accepted: 21 April 2014
Published: 16 September 2014
Authors
Alexandru Chirvasitu
Department of Mathematics
University of Washington
Box 354350
Seattle, WA 98195-4350
United States