Algebraic Structures Related to The Dynamical Yang-Baxter Equation

A solution to the set-theoretic Yang-Baxter Equation (YBE) is a braided set. Analogously, a solution to the quiver-theoretic Dynamical Yang-Baxter Equation (DYBE) will be a braided quiver. Solutions to the DYBE are called 'Dynamical Yang-Baxter maps' (DYBMs). DYBMs are associated with two relevant algebraic objects: the structure category and the structure groupoid. In this thesis, we describe examples of DYBMs, and investigate the structure category and groupoid. Among the examples, we focus in particular on dynamical braces, and prove some original results providing a better description of their associated quivers. In a second part, we prove that the structure groupoid of an involutive non-degenerate DYBM is Garside. This generalises a well-known result by Chouraqui. At the end, we describe a topological interpretation for the structure groupoid