Ref HAL: hal-00670317_v1
Ref Arxiv: 1202.2312
DOI: 10.1016/j.geomphys.2012.05.008
WoS: 000307610700002
Ref. & Cit.: NASA ADS
Exporter : BibTex | endNote
17 Citations
Résumé:

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.