4 papers
Center of generalized skein algebras
Hiroaki Karuo, Han-Bom Moon, Helen Wong
We consider a generalization of the Kauffman bracket skein algebra of a surface that is generated by loops and arcs between marked points on the interior or boundary, up to skein r…
Azumaya loci of skein algebras
Hiroaki Karuo, Julien Korinman
We compute the Azumaya loci of Kauffman-bracket skein algebras of closed surfaces at odd roots of unity and provide partial results for open surfaces as well. As applications, we g…
Cluster algebras and skein algebras for surfaces
Hiroaki Karuo, Han-Bom Moon, Helen Wong
We consider two algebras of curves associated to an oriented surface of finite type - the cluster algebra from combinatorial algebra, and the skein algebra from quantum topology. W…
Quantum duality maps, skein algebras and their ensemble compatibility
Tsukasa Ishibashi, Hiroaki Karuo
We generalize the quantum duality map of Allegretti--Kim [AK17] for punctured closed surfaces to general marked surfaces. When the marked surface has no…