The Yang-Baxter equation is the key to integrability for lattice models in statistical mechanics on a two-dimensional lattice. Its algebraic aspects are now well understood in terms of quantum groups. The Tetrahedron equation is a generalization to the three dimensional system, which is more challenging but has seen many interesting developments. I will give a brief introduction to the subject and present some new results based q-Weyl algebra valued six-vertex models.

(Based on a joint work with Shuichiro Matsuike and Akihito Yoneyama.)