Yangians and Classical Lie Algebras

TL;DR

This paper explores the detailed structure of Yangians associated with classical Lie algebras, including new twisted Yangian algebras, which are quantum deformations of polynomial Lie algebras.

Contribution

It provides a detailed analysis of Yangians and introduces twisted Yangians related to classical Lie algebra series, expanding the understanding of their algebraic structures.

Findings

Yangian Y(gl(N)) is a quantum deformation of U(gl(N)[x])

Introduction of twisted Yangians associated with B, C, D series

Enhanced understanding of the algebraic structure of Yangians and twisted Yangians

Abstract

We study in detail the structure of the Yangian Y(gl(N)) and of some new Yangian-type algebras called twisted Yangians. The algebra Y(gl(N)) is a `quantum' deformation of the universal enveloping algebra U(gl(N)[x]), where gl(N)[x] is the Lie algebra of gl(N)-valued polynomial functions. The twisted Yangians are quantized enveloping algebras of certain twisted Lie algebras of polynomial functions which are naturally associated to the B, C, and D series of the classical Lie algebras.