Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 13 (2017), 011, 35 pages      arXiv:1401.2143      https://doi.org/10.3842/SIGMA.2017.011
Contribution to the Special Issue on Recent Advances in Quantum Integrable Systems

Drinfeld J Presentation of Twisted Yangians

Samuel Belliard a and Vidas Regelskis bc
a) Institut de Physique Théorique, Orme des Merisiers batiment 774, CEA/DSM/IPhT, CEA/Saclay, F-91191 Gif-sur-Yvette Cedex, France
b) Department of Mathematics, University of York, Heslington, York, YO10 5DD, UK
c) Department of Mathematics, University of Surrey, Guildford, GU2 7XH, UK

Received May 24, 2016, in final form February 21, 2017; Published online March 01, 2017

Abstract
We present a quantization of a Lie coideal structure for twisted half-loop algebras of finite-dimensional simple complex Lie algebras. We obtain algebra closure relations of twisted Yangians in Drinfeld J presentation for all symmetric pairs of simple Lie algebras and for simple twisted even half-loop Lie algebras. We provide the explicit form of the closure relations for twisted Yangians in Drinfeld J presentation for the ${\mathfrak{sl}}_3$ Lie algebra.

Key words: coideal; coisotropic subalgebra; deformation; Manin triple; twisted Yangians.

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