Title: From Yangians to Yangian doubles
Speaker: Curtis Wendlandt (University of Alberta)
Abstract: The Yangian $Y(\mathfrak{g})$ of a complex semisimple Lie algebra $\mathfrak{g}$ is a remarkable Hopf algebra which arises as a quantization of the standard Lie bialgebra structure on $\mathfrak{g}[t]$. An elementary result of fundamental importance to the theory of Yangians is that $Y(\mathfrak{g})$ has a family of automorphisms, indexed by the complex numbers, which quantize the automorphisms of $\mathfrak{g}[t]$ given by shifting $t$ by a complex scalar. These are the so-called shift automorphisms of the Yangian.
A small modification to the definition of the Yangian leads to a larger algebra called the Yangian double (denoted $DY(\mathfrak{g})$) which, in principle, should encode additional symmetries of the Yangian itself. In this talk, I will explain how the aforementioned shift automorphisms lead to a family of injections from $DY(\mathfrak{g})$ into a completion of $Y(\mathfrak{g})$ which can be used to exploit surprisingly deep connections between Yangians, Yangian doubles, and quantum loop algebras.
Seminar URL: https://research.math.osu.edu/reps/