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| HAL : hal-00670317, version 1 |
| arXiv : 1202.2312 |
| DOI : 10.1016/j.geomphys.2012.05.008 |
| Fiche détaillée |  Récupérer au format |
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| Journal of Geometry and Physics 62, 10 (2012) 2009 |
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| Coideal algebras from twisted Manin triples |
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| Nicolas Crampé 1Samuel BELLIARD 1 |
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| (17/10/2012) |
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| We propose a new approach to study coideal algebras. It is well-known that Manin triples (or equivalently Lie bi-algebra structures) are the requirement to deform Lie algebras and to obtain quantum groups. In this paper, introducing some particular automorphisms of Manin triples, we define new structures that we call Lie bi-ideal structures. A link with coisotropic subalgebras is explained. We show that their deformation provide coideal algebras. As examples, we recover from our general construction the twisted Yangians, the q-Onsager algebra and the augmented q-Onsager algebra. As an important by-product, we find a new presentation for the twisted Yangians. |
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| 1 : | Laboratoire Charles Coulomb (L2C) |
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CNRS : UMR5221 – Université Montpellier II - Sciences et techniques |
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| Domaine | : | Mathématiques/Algèbres quantiques Physique/Physique mathématique Mathématiques/Physique mathématique |
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| Coideal – Coisotropic subalgebra – Deformation – Manin triple – Onsager algebras – Twisted Yangians – Reflection algebras |
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| Lien vers le texte intégral : |
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| http://fr.arXiv.org/abs/1202.2312 |
| hal-00670317, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00670317 | |
| oai:hal.archives-ouvertes.fr:hal-00670317 | |
| Contributeur : L2c Aigle | |
| Déposé pour le compte de : | |
| Soumis le : Mercredi 15 Février 2012, 10:55:21 | |
| Dernière modification le : Mardi 17 Juillet 2012, 10:54:53 | |
