\(F\)-polynomials in quantum cluster algebras. (Q763383)

A quantum cluster algebra is a noncommutative deformation of a cluster algebra. In the present paper the author shows existence of quantum \(F\)-polynomials for quantum cluster algebras. These polynomials have the property that any cluster variable in a quantum cluster algebra may be computed (up to a power of the deformation parameter \(q\)) from the initial extended cluster using quantum \(F\)-polynomials. Specialization \(q=1\) recovers the classical case. The paper also provides a recursive formula for computation of quantum \(F\)-polynomials. For type \(A\) quantum cluster algebras the paper gives an explicit formula for all corresponding quantum \(F\)-polynomials.