Hopf algebra actions on strongly separable extensions of depth two
| dc.creator | Kadison, Lars | |
| dc.creator | Nikshych, Dmitri | |
| dc.date | 2001-07-09 | |
| dc.date.accessioned | 2026-07-07T04:42:32Z | |
| dc.date.available | 2026-07-07T04:42:32Z | |
| dc.description | We bring together ideas in analysis of Hopf *-algebra actions on II_1 subfactors of finite Jones index and algebraic characterizations of Frobenius, Galois and cleft Hopf extensions to prove a non-commutative 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 k-algebras split as N-bimodules with a trivial centralizer C_M(N). Let M_1 := End(M)_N and M_2 := End(M_1)_M be the endomorphism algebras in the Jones tower N < M < M_1 < M_2. We show that under depth 2 conditions on the second centralizers A := C_{M_1}(N) and B : = C_{M_2}(M) the algebras A and B are semisimple Hopf algebras dual to one another and such that M_1 is a smash product of M and A, and that M is a B-Galois extension of N. | |
| dc.description | 21 pages, ams-latex; to appear in Advances in Mathematics | |
| dc.identifier | https://arxiv.org/abs/math/0107064 | |
| dc.identifier | http://arxiv.org/abs/math/0107064 | |
| dc.identifier | Adv. Math. 163 (2001), no. 2, 258--286 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/61821 | |
| dc.subject | Rings and Algebras | |
| dc.subject | Quantum Algebra | |
| dc.subject | 12F10,16W30, 22D30, 46L37 | |
| dc.title | Hopf algebra actions on strongly separable extensions of depth two | |
| dc.type | text |