Séminaires : Séminaire d'Algèbre

We introduce quantum cluster algebras over arbitrary commutative rings. We also present a general method to construct (partially compactified) quantum cluster structures on quantized coordinate rings from those defined on localizations, in a setting where the standard codimension-two arguments used in the classical case are no longer available.

As an application, we obtain natural quantum cluster structures on the quantized coordinate rings of all simple algebraic groups over arbitrary commutative rings. This is based on a series of joint papers with Milen Yakimov and Hironori Oya.

This talk will take place in hybrid mode at the Institut Henri Poincaré.