Description:A cluster algebra is a kind of commutative algebra with a distinguished set of generators organized into overlapping finite subsets called clusters. Though the definition of a cluster algebra seems strange at first encounter, these algebras appear naturally in many areas of mathematics. In the two decades since they were first discovered, cluster algebras have been used to study top...
AbstractWe present a rigid cluster model to realize the quantum group $U_q(g)$ for $g$ of type ADE. That is, we prove that there is a natural Hopf algebra isomorphism from the quantum group to a quotient algebra of the Weyl group invariants of a Fock-Goncharov quantum cluster algebra. By applying the quantum duality of cluster algebras, we show that the quantum group admits a cluster canonical ...
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