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Fermion realizations of generalized Kac–Moody and Virasoro algebras associated to the two-sphere and the two-torus
By using the notion of extension of Kac–Moody algebras for higher-dimensional compact manifolds recently introduced, we show that for the two-torus [Formula: see text] and the two-sphere [Formula: see text], these extensions, as well as extensions of the Virasoro algebra can be obtained naturally from the usual Kac–Moody and Virasoro …