Coideal algebras from twisted Manin triple

Details Coideal algebras from twisted Manin triple Coideal algebras from twisted Manin triple

2012-02-10

arxiv.org/abs/1202.2312v2

Mathematics

Quantum Algebra

Scientific paper

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.

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