PIMS-USask Geometry, Algebra and Physics Seminar: Bryan Kettle

Given any finite-dimensional simple Lie algebra a over \(\mathbb{C}\), the Yangian \(Y(a)\) is a certain unital associative \(\mathbb{C}\)-algebra. In particular, Yangians form a family of so-called quantum groups. The main property these algebras is the foundational fact that their representations produce rational solutions to the quantum Yang-Baxter equation. The structure and representation theory of Yangians has become a study in and of itself and has expanded to the study of super Yangians based on Lie superalgebras; however, the theory of super Yangians is comparatively less developed than its non-super counterpart. In this talk, we will survey what recent advancements have been made in the study of super Yangians and view what else remains to do.