The A-polynomial from the noncommutative viewpoint
The authors introduce a noncommutative generalization of the A-polynomial of a knot, called the noncommutative A-ideal. It consists of a finitely generated ideal of polynomials in the quantum plane. For their construction, the authors use the fact that the Kauffman bracket skein algebra of the cylinder over the torus is a subalgebra of the noncommutative torus.NEWLINENEWLINENEWLINESome properties of the noncommutative A-ideal and its relationships with the A-polynomial and the Jones polynomial are discussed.
scientific article; zbMATH DE number 1680732