Quadratic algebras and their Casimir invariants

Quadratic algebras are generalisations of Lie algebras that have appeared in a variety of contexts of mathematical physics over the last 20 years. They play a central role in certain classes of exactly solvable systems, and are related to special functions and orthogonal polynomials in pure mathematics. This project aims to describe their universal enveloping algebras and obtain the so-called Casimir invariants.