Toroidal Cluster Algebra and the Toroidal Grothendieck ring of a tensor category

Abstract: Let U be the quantum loop algebra corresponding to a simple Lie algebra and K be the Grothendieck ring of a specific tensor category consisting of finite-dimensional U-modules, which possesses a natural cluster algebra structure. In this talk, we delineate a toroidal cluster structure endowed with two parameters on the toroidal Grothendieck ring K of the monomial category C, which is intimately tied to the quantum loop algebra of type A3.

quantum algebrarings and algebras

Audience: researchers in the topic

European Non-Associative Algebra Seminar