Séminaire de Physique ThéoriqueManin triples twist and coideal algebras
Samuel Belliard (Montpellier)
Friday 06 April 2012 14:00 - Tours - Salle 1180 (Bât E2)
The algebraic structures that lead to the integrability of quantum integrable models are given by quantum groups (for models on a line or on a circle) and by coideal algebras (for models on a segment or on a half-line). Quantum groups can be constructed from the quantification of Universal Lie algebras. This procedure, introduced by Drinfel'd in 1985, uses the notion of bialgebras or equivalently of Manin triples. In a resent paper, (arxiv:1202.2312 in collaboration with N. Crampé) we introduced the notion of Manin triples twist and gave a procedure to construct coideal algebras from Universal Lie sub-algebras. We will review Drinfel'd quantification procedure and present our quantification procedure to obtain coideal algebras. Some applications to quantum integrable models will be discussed.