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Hopf algebra actions on strongly separable extensions of depth two
 Adv. in Math. 163
, 2001
"... Abstract. We bring together ideas in analysis of Hopf ∗algebra actions on II1 subfactors of finite Jones index [9, 24] and algebraic characterizations of Frobenius, Galois and cleft Hopf extensions [14, 13, 3] to prove a noncommutative algebraic analogue of the classical theorem: a finite field ex ..."
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Cited by 21 (20 self)
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Abstract. We bring together ideas in analysis of Hopf ∗algebra actions on II1 subfactors of finite Jones index [9, 24] and algebraic characterizations of Frobenius, Galois and cleft Hopf extensions [14, 13, 3] to prove a noncommutative algebraic analogue of the classical theorem: a finite field extension is Galois iff it is separable and normal. Suppose N ֒ → M is a separable Frobenius extension of kalgebras split as Nbimodules with a trivial centralizer CM(N). Let M1: = End(MN) and M2: = End(M1)M be the endomorphism algebras in the Jones tower N ֒ → M ֒ → M1 ֒ → M2. We show that under depth 2 conditions on the second centralizers A: = CM1 (N) and B: = CM2 (M) the algebras A and B are semisimple Hopf algebras dual to one another and such that M1 is a smash product of M and A, and that M is a BGalois extension of N. 1.
Lagrange’s theorem for Hopf monoids in species
, 2012
"... Abstract. Following Radford’s proof of Lagrange’s theorem for pointed Hopf algebras, ..."
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Cited by 4 (3 self)
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Abstract. Following Radford’s proof of Lagrange’s theorem for pointed Hopf algebras,