Vol. 8, No. 5, 2014

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Cosemisimple Hopf algebras are faithfully flat over Hopf subalgebras

Alexandru Chirvasitu

Vol. 8 (2014), No. 5, 1179–1199

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.

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
Received: 11 August 2013
Revised: 6 March 2014
Accepted: 21 April 2014
Published: 16 September 2014
Alexandru Chirvasitu
Department of Mathematics
University of Washington
Box 354350
Seattle, WA 98195-4350
United States