Center of generalized skein algebras

Abstract

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 relations defined by Muller and Roger-Yang. We compute the center of this Muller-Roger-Yang skein algebra and show that it is almost Azumaya when the quantum parameter $q$ is a primitive $n$-th root of unity with odd $n$. We also discuss the implications on the representation theory of the Muller-Roger-Yang generalized skein algebra.