Star product and q-deformation of Grassmann and symmetric algebras

We review the relation between the star product on a Poisson-Lie group and the quantum Yang-Baxter equation. We define the q-deformed Grassmann and q-deformed symmetric algebras on a vector space V, and prove that a star product on a triangular (simple quasitriangular) Poisson-Lie group G determines a q-deformation of both the symmetric and Grassmann algebras over a dual of a g-module where g is the corresponding triangular (simple quasitriangular) Lie bialgebra of the Poisson-Lie group G.