Nicolas Crampe, Samuel Belliard
We propose a new approach to study coideal algebras. It is well-known that
Manin triples (or equivalently Lie bi-algebra structure) is the requirement to
deform Lie algebra and to obtain quantum groups. In this paper, introducing
some particular automorphisms of Manin triples, we define a new structure that
we call Lie bi-ideal structure. 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.
View original:
http://arxiv.org/abs/1202.2312
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