The [formula omitted] crystal for a family of generalized quantum groups

Abstract

In [1] Bozec gave a definition of generalized quantum groups that extends the usual definition of quantum groups to finite quivers with loops at vertices, and in [3] he introduced a theory of generalized crystals for this new family of Hopf algebras. We explicitly characterize the generalized crystal B(∞) associated to a certain family of comet-shaped quivers with multiple loops by providing a complete set of relations among the Kashiwara operators themselves.