Hopf-Galois coextensions and braided Lie coalgebras

摘要

＜正＞ Let k be a commutative ring and H a k-bialgebra. Assume that there exists an H-cogalois right H-module coalgebra C such that C is faithfully k-flat. We show that H is necessarily a Hopf algebra. Then the Lie coalgebras in Yetter-Drinfeld categoriesHHYD （braided Lie coalgebras） are studied. In particular, a necessary and sufficient condition for the natural map ГC（ UCM）→M to be surjec-tive is given.