Quantum Laurent Polynomials: Classes and Representations

Quantum polynomials play an important role in noncommutative geometry. This work combines the algebraic and geometric approaches to this subject. As with the Weyl algebras, there exist nonholonomic simple modules with the maximum possible Gelfand--Kirillov dimension. Some algebras of quantum Laurent polynomials which possess an impervious module virtually decompose as a tensor product of algebras.