Mathematical Sciences: Lie Algebras and Vertex Operator Algebras

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This project is concerned with Lie algebras and vertex operator algebras. The principal investigators plan to find relations between the classical and Lie theoretic proofs of the Rogers-Ramanujan identities by studying vertex operator algebras from the viewpoint of monodromy and Virasoro algebra theory. In addition, they will study Monstrous Moonshine and look for structure theorems on Lie algebras of prime characteristic which will simplify the proof of the classification theorem. The research supported concerns the representation theory of Lie algebras and is focused on both the structure of these algebras and the applications of these algebras to questions in theoretical physics. Beginning with works of Lie, Killing, and Cartan, the theory of finite-dimensional Lie algebras has been developed for the past 100 years and provides a necessary background for every mathematician and physicist.