$K_{\mathfrak{q}}$-algebras

Abstract

We introduce the notion of $K_{\mathfrak{q}}$-algebra, a conjectural axiomatization of the fusion algebra of rotation-equivariant BPS line defects in a 4d ${\cal N}=2$ Supersymmetric Quantum Field Theory. We also introduce the notion of RG flow of $K_{\mathfrak{q}}$-algebras, a conjectural axiomatization of the action of Seiberg-Witten type RG flows on line defects. These definitions enrich the theory of cluster algebras, $K$-theoretic Coulomb branch algebras, skein algebras and quantum groups.