A Kac-Moody algebra is a type of infinite-dimensional Lie algebra that arises from generalizing finite-dimensional semisimple Lie algebras. These algebras are defined by their root systems and can be used to study representations, integrable systems, and mathematical physics. Kac-Moody algebras play a significant role in various fields, such as representation theory and string theory, due to their rich structure and connections to geometry.
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