Kac–Moody algebra

Kac–Moody algebras are a class of infinite-dimensional Lie algebras that generalize the concept of finite-dimensional semisimple Lie algebras. They are named after Victor G. Kac, who introduced them in the 1960s as a way to study certain symmetries in mathematical physics and representation theory. A Kac–Moody algebra is defined by a generalized Cartan matrix, which captures the relationships between the root system of the algebra.