Representations of Uq(Lsl2)Uq(Lsl2) at roots of unity and generalised cluster algebras

We show that the Grothendieck rings of finite-dimensional representations of the quantum loop algebra of sl2sl2 at roots of unity have the combinatorial structure of a generalised cluster algebra of type CC. Moreover, we show that the classes of simple objects in the Grothendieck ring essentially coincide with the cluster monomials. We also state a conjecture for Uεres(Lsl3), and prove it when the root of unity is of order 2.