Milen Yakimov -- Root of unity quantum cluster algebras, Cayley-Hamilton algebras, and discriminants
Author information
- Milen Yakimov
- Northeastern University
- Website: https://cos.northeastern.edu/people/mike-yakimov/
Abstract:
Cluster Algebras were defined by Fomin and Zelevinsky twenty years ago, and since then have played a key role in many areas of mathematics and mathematical physics. We will present a gentle introduction to the subject and describe a framework for root of unity quantum cluster algebras, which gives a uniform approach to various important families of algebras from Lie theory and topology. We will show that they have canonical trace maps turning them into Cayley-Hamilton algebras. Such algebras have discriminants given by a generalization of Dedekind’s construction for number fields. An effective way for computing these discriminants will be presented. This is a joint work with Shengnan Huang, Thang Le, Bach Nguyen and Kurt Trampel.