The Endomorphism Ring Theorem for Galois and D2 extensions
| dc.creator | Kadison, Lars | |
| dc.date | 2005-03-10 | |
| dc.date | 2005-04-01 | |
| dc.date.accessioned | 2026-07-07T05:17:51Z | |
| dc.date.available | 2026-07-07T05:17:51Z | |
| dc.description | Let $S$ be the left bialgebroid $\End {}_BA_B$ over the centralizer $R$ of a right D2 algebra extension $A \| B$, which is to say that its tensor-square is isomorphic as $A$-$B$-bimodules to a direct summand of a finite direct sum of $A$ with itself. We prove that its left endomorphism algebra is a left $S$-Galois extension of $A^{\rm op}$. As a corollary, endomorphism ring theorems for D2 and Galois extensions are derived from the D2 characterization of Galois extension (cf. math.QA/0502188 and math.QA/0409589). We note the converse that a Frobenius extension satisfying a generator condition is D2 if its endomorphism algebra extension is D2. | |
| dc.description | 20 pp, some additional material including a converse endomorphism ring theorem for certain Frobenius extensions, which yields a complete answer to question 1 in math.RA/0107064 | |
| dc.identifier | https://arxiv.org/abs/math/0503194 | |
| dc.identifier | http://arxiv.org/abs/math/0503194 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/74457 | |
| dc.subject | Quantum Algebra | |
| dc.subject | 13B05, 16S40, 20L05, 81R50 | |
| dc.title | The Endomorphism Ring Theorem for Galois and D2 extensions | |
| dc.type | text |