THE FAITHFUL FLATNESS OF HOPF ALGEBRAS OVER COIDEAL SUBALGEBRAS WITH CONDITIONAL EXPECTATION

Faithful flatness is an algebraic concept arising from algebraic geometry and closely related to the question of forming ''good'' quotients. Also, it plays a key role in the noncommutative world, especially in Hopf-algebra theory. After a review of its use and of what is known about the question of faithful flatness over Hopf subalgebras or coideal subalgebras, I will present and explain a new result concerning the faithful flatness of a Hopf algebra over a coideal subalgebra having a conditional expectation.