The Yang-Baxter relation and gauge invariance

Starting from a quantum dilogarithm over a Pontryagin self-dual LCA group $A$, we construct an operator solution of the Yang-Baxter equation generalizing the solution of the Faddeev-Volkov model. Based on a specific choice of a subgroup $B\subset A$ and by using the Weil transformation, we also give a new non-operator interpretation of the Yang-Baxter relation. That allows us to construct a lattice QFT-model of IRF-type with gauge invariance under independent $B$-translations of local `spin’ variables.