Galois theory for bialgebroids, depth two and normal Hopf subalgebras
| dc.creator | Kadison, Lars | |
| dc.date | 2005-02-09 | |
| dc.date.accessioned | 2026-07-07T05:16:50Z | |
| dc.date.available | 2026-07-07T05:16:50Z | |
| dc.description | We reduce certain proofs in math.RA/0108067, math.RA/0408155, and math.QA/0409589 to depth two quasibases from one side only, a minimalistic approach which leads to a characterization of Galois extensions for finite projective bialgebroids without the Frobenius extension property. We prove that a proper algebra extension is a left $T$-Galois extension for some right finite projective left bialgebroid over some algebra $R$ if and only if it is a left depth two and left balanced extension. Exchanging left and right in this statement, we have a characterization of right Galois extensions for left finite projective right bialgebroids. Looking to examples of depth two, we establish that a Hopf subalgebra is normal if and only if it is a Hopf-Galois extension. We characterize finite weak Hopf-Galois extensions using an alternate Galois canonical mapping with several corollaries: that these are depth two and that surjectivity of the Galois mapping implies its bijectivity. | |
| dc.description | 19 pp., to appear in Proceedings of the "Ferrara Algebra Workshop" jointly with the "Workshop on Hopf Algebras,Swansea" (to be published as a special issue of the "Annali dell'Universita' di Ferrara, sez. VII, Scienze Matematiche) | |
| dc.identifier | https://arxiv.org/abs/math/0502188 | |
| dc.identifier | http://arxiv.org/abs/math/0502188 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/74134 | |
| dc.subject | Quantum Algebra | |
| dc.subject | Rings and Algebras | |
| dc.subject | 16W30 (13B05, 16S40, 20L05, 81R50) | |
| dc.title | Galois theory for bialgebroids, depth two and normal Hopf subalgebras | |
| dc.type | text |