Twisted Yangians of small rank

TL;DR

This paper investigates small-rank twisted Yangians related to symmetric pairs, establishing isomorphisms with known algebraic structures and connecting different presentations of these algebras.

Contribution

It provides new isomorphisms between twisted Yangians of small rank and established algebraic structures, unifying various presentations.

Findings

Isomorphisms with Olshanskii's twisted Yangians of types AI and AII

Connections with Molev-Ragoucy reflection algebras of type AIII

Equivalence with twisted Yangians in Drinfeld's presentation

Abstract

We study quantized enveloping algebras called twisted Yangians associated with the symmetric pairs of types CI, BDI and DIII (in Cartan's classification) when the rank is small. We establish isomorphisms between these twisted Yangians and the well known Olshanskii's twisted Yangians of types AI and AII, and also with the Molev-Ragoucy reflection algebras associated with symmetric pairs of type AIII. We also construct isomorphisms with twisted Yangians in Drinfeld's original presentation.