Twisted Yangians for symmetric pairs of types B, C, D

TL;DR

This paper investigates twisted Yangians linked to symmetric pairs of types B, C, D, establishing their algebraic properties, centers, and relations to reflection algebras within the framework of quantum groups.

Contribution

It introduces a detailed study of twisted Yangians for types B, C, D, including their algebraic structure, centers, and connections to reflection algebras, extending previous understanding in quantum algebra.

Findings

Proved an analogue of the Poincare-Birkoff-Witt theorem for these algebras

Determined the centers of twisted Yangians

Analyzed the structure of extended reflection algebras

Abstract

We study a class of quantized enveloping algebras, called twisted Yangians, associated with the symmetric pairs of types B, C, D in Cartan's classification. These algebras can be regarded as coideal subalgebras of the extended Yangian for orthogonal or symplectic Lie algebras. They can also be presented as quotients of a reflection algebra by additional symmetry relations. We prove an analogue of the Poincare-Birkoff-Witt Theorem, determine their centres and study also extended reflection algebras.