Finite presentations for stated skein algebras and lattice gauge field theory

TL;DR

This paper establishes finite presentations for stated skein algebras, proves their Koszul property, and shows their isomorphism to quantum moduli algebras in lattice gauge field theory, extending prior results.

Contribution

It provides finite algebraic presentations and links skein algebras to quantum moduli algebras, broadening understanding in quantum topology and gauge theory.

Findings

Stated skein algebras have finite presentations.

These algebras are Koszul.

They are isomorphic to quantum moduli algebras.

Abstract

We provide finite presentations for stated skein algebras and deduce that those algebras are Koszul and that they are isomorphic to the quantum moduli algebras appearing in lattice gauge field theory, generalizing previous results of Bullock, Frohman, Kania-Bartoszynska and Faitg.