Classical dynamical r-matrices, Poisson homogeneous spaces, and Lagrangian subalgebras
| dc.creator | Karolinsky, Eugene | |
| dc.creator | Stolin, Alexander | |
| dc.date | 2001-10-30 | |
| dc.date | 2002-02-12 | |
| dc.date.accessioned | 2026-07-07T04:44:09Z | |
| dc.date.available | 2026-07-07T04:44:09Z | |
| dc.description | Jiang-Hua Lu showed that any dynamical r-matrix for the pair $(g,u)$ naturally induces a Poisson homogeneous structure on $G/U$. She also proved that if $g$ is complex simple, $u$ is its Cartan subalgebra and $r$ is quasitriangular, then this correspondence is in fact 1-1. In the present paper we find some general conditions under which the Lu correspondence is 1-1. Then we apply this result to describe all triangular Poisson homogeneous structures on $G/U$ for a simple complex group $G$ and its reductive subgroup $U$ containing a Cartan subgroup. | |
| dc.description | LaTeX, 20 pages. We add a method that allows to get constant r-matrices from dynamical ones (see Appendix B) | |
| dc.identifier | https://arxiv.org/abs/math/0110319 | |
| dc.identifier | http://arxiv.org/abs/math/0110319 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/62520 | |
| dc.subject | Quantum Algebra | |
| dc.title | Classical dynamical r-matrices, Poisson homogeneous spaces, and Lagrangian subalgebras | |
| dc.type | text |