Quantum elliptic algebras and double Yangians
| dc.creator | Frappat, L. | |
| dc.date | 2002-01-25 | |
| dc.date | 2002-04-09 | |
| dc.date.accessioned | 2026-07-07T04:46:06Z | |
| dc.date.available | 2026-07-07T04:46:06Z | |
| dc.description | Quantum universal enveloping algebras, quantum elliptic algebras and double (deformed) Yangians provide fundamental algebraic structures relevant for many integrable systems. They are described in the FRT formalism by R-matrices which are solutions of elliptic, trigonometric or rational type of the Yang--Baxter equation with spectral parameter or its generalization known as the Gervais--Neveu--Felder equation. While quantum groups and double Yangians appear as quasi-triangular Hopf algebras, this is no longer the case for elliptic algebras and the various deformations of Yangian type algebras. These structures are dealt with the framework of quasi-Hopf algebras. These algebras can be obtained from Hopf algebras through particular Drinfel'd twists satisfying the so-called shifted cocycle condition. We review these different structures and the pattern of connections between them. | |
| dc.description | 50 pages - Lectures given at the First French-Moroccan School on Non-Commutative Geometry at Marseilles (France), december 2001 - Misprints corrected | |
| dc.identifier | https://arxiv.org/abs/math/0201245 | |
| dc.identifier | http://arxiv.org/abs/math/0201245 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/63201 | |
| dc.subject | Quantum Algebra | |
| dc.subject | 81R50, 17B37 | |
| dc.title | Quantum elliptic algebras and double Yangians | |
| dc.type | text |