Coideal algebras from twisted Manin triples

Abstract

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.

References in corpus (5)

• Hidden Grassmann structure in the XXZ model
• On universal solution to reflection equation
• Generalized q-Onsager Algebras and Dynamical K-matrices
• Reflection equation and twisted Yangians
• Quantization of coisotropic subalgebras in complex semisimple Lie Algebras

Cited by in corpus (15)

• Integrable approach to simple exclusion processes with boundaries. Review and progress
• Equivalences between three presentations of orthogonal and symplectic Yangians
• Integrable systems from the classical reflection equation
• Twisted Yangians for symmetric pairs of types B, C, D
• Non-Abelian symmetries of the half-infinite XXZ spin chain
• FRT presentation of the Onsager algebras
• Gauge Theory and Boundary Integrability
• An action of the free product ${\mathbb{Z}}_2\star {\mathbb{Z}}_2\star {\mathbb{Z}}_2$ on the $q$-Onsager algebra and its current algebra
• The $q$-Onsager algebra and the positive part of $U_q({\widehat{\mathfrak{sl}}}_2)$
• Twisted Yangians of small rank
• Truncation of the reflection algebra and the Hahn algebra
• Drinfeld J Presentation of Twisted Yangians
• Higher rank classical analogs of the Askey-Wilson algebra from the $s{l}_N$ Onsager algebra
• Reflection algebras for sl(2) and gl(1|1)
• Twisted Yangian symmetry of the open Hubbard model