Representations of the Quantized Function Algebras, 2-Categories and Zamolodchikov Tetrahedra Equation

Abstract

For any complex simply connected simple Lie group G one can define a quantization $\overline {\Bbb C} \left[ G \right]$ of the algebra ℂ[G] regular functions on G as a Hopf algebra over the ring ℂ[q,q ^-1] of Laurent polynomials (see [Lu]). Let t be a nonzero complex number, and let ℂ_t be a one-dimensional complex vector space equipped with a structure of ℂ[q,q ^-1]-module such that q acts as multiplication on t.