Hopf algebroids and Galois extensions
| dc.creator | Kadison, Lars | |
| dc.date | 2004-09-07 | |
| dc.date.accessioned | 2026-07-07T05:11:52Z | |
| dc.date.available | 2026-07-07T05:11:52Z | |
| dc.description | To a finite Hopf-Galois extension $A | B$ we associate dual bialgebroids $S := \End_BA_B$ and $T := (A ø_B A)^B$ over the centralizer $R$ using the depth two theory in math.RA/0108067. First we extend results on the equivalence of certain properties of Hopf-Galois extensions with corresponding properties of the coacting Hopf algebra \cite{KT,Doi} to depth two extensions using coring theory math.RA/0002105. Next we show that $T^{\rm op}$ is a Hopf algebroid over the centralizer $R$ via Lu's theorem 5.1 in math.QA/9505024 for smash products with special modules over the Drinfel'd double, the Miyashita-Ulbrich action, the fact that $R$ is a commutative algebra in the pre-braided category of Yetter-Drinfel'd modules \cite[Schauenburg]{Sch} and the equivalence of Yetter-Drinfel'd modules with modules over Drinfel'd double \cite[Majid]{Maj}. In our last section, an exposition of results of Sugano \cite{Su82,Su87} leads us to a Galois correspondence between sub-Hopf algebroids of $S$ over simple subalgebras of the centralizer with finite projective intermediate simple subrings of a finite projective H-separable extension of simple rings $A \supseteq B$. | |
| dc.description | 19 pages, to appear in the Bulletin of the Belgian Mathematical Society - Simon Stevin in approx. the second issue of 2005 | |
| dc.identifier | https://arxiv.org/abs/math/0409106 | |
| dc.identifier | http://arxiv.org/abs/math/0409106 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/72393 | |
| dc.subject | Quantum Algebra | |
| dc.subject | Commutative Algebra | |
| dc.subject | Rings and Algebras | |
| dc.subject | 06A15, 12F10, 13B02, 16W30 | |
| dc.title | Hopf algebroids and Galois extensions | |
| dc.type | text |