Fundamentals of Poisson Lie Groups with Application to the Classical Double
| dc.creator | Ahluwalia, K. S. | |
| dc.date | 1993-10-13 | |
| dc.date | 1994-03-12 | |
| dc.date.accessioned | 2026-07-07T09:01:22Z | |
| dc.date.available | 2026-07-07T09:01:22Z | |
| dc.description | We give a constructive account of the fundamental ingredients of Poisson Lie theory as the basis for a description of the classical double group $D$. The double of a group $G$ has a pointwise decomposition $D\sim G\times G^*$, where $G$ and $G^*$ are Lie subgroups generated by dual Lie algebras which form a Lie bialgebra. The double is an example of a factorisable Poisson Lie group, in the sense of Reshetikhin and Semenov-Tian-Shansky [1], and usually the study of its Poisson structures is developed only in the case when the subgroup $G$ is itself factorisable. We give an explicit description of the Poisson Lie structure of the double without invoking this assumption. This is achieved by a direct calculation, in infinitesimal form, of the dressing actions of the subgroups on each other, and provides a new and general derivation of the Poisson Lie structure on the group $G^*$. For the example of the double of SU(2), the symplectic leaves of the Poisson Lie structures on SU(2) and SU(2$)^*$ are displayed. | |
| dc.description | 30 pages. Principal content unaltered, some misprints corrected some statements reworded, three references added, format expanded (reversible) | |
| dc.identifier | https://arxiv.org/abs/hep-th/9310068 | |
| dc.identifier | http://arxiv.org/abs/hep-th/9310068 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/148296 | |
| dc.subject | High Energy Physics - Theory | |
| dc.subject | Quantum Algebra | |
| dc.title | Fundamentals of Poisson Lie Groups with Application to the Classical Double | |
| dc.type | text |