KacMoody
Kac–Moody algebras are a broad class of Lie algebras that generalize finite-dimensional semisimple Lie algebras to infinite dimensions. They are defined from a generalized Cartan matrix and were developed independently by Victor Kac and Robert Moody in the late 1960s and early 1970s. The construction provides a unifying framework for many infinite-dimensional symmetry algebras that appear in mathematics and theoretical physics.
A Kac–Moody algebra is built from generators e_i, f_i, h_i for i = 1,…,n, subject to standard Cartan
Classification by the generalized Cartan matrix A leads to several types. If A is positive definite, the
Representations of Kac–Moody algebras include highest-weight modules, many of which are infinite-dimensional but retain structure analogous