Quantum affine algebra

In mathematics, a quantum affine algebra (or affine quantum group) is a Hopf algebra that is a "q"-deformation of the universal enveloping algebra of an affine Lie algebra. They were introduced independently by and as a special case of their general construction of a quantum group from a Cartan matrix. One of their principal applications has been to the theory of solvable lattice models in quantum statistical mechanics, where the Yang–Baxter equation occurs with a spectral parameter. Combinatorial aspects of the representation theory of quantum affine algebras can be described simply using crystal bases, which correspond to the degenerate case when the deformation parameter "q" vanishes and the Hamiltonian of the associated lattice model can be explicitly diagonalized.