Integrability of C2-Cofinite Vertex Operator Algebras

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【标题】Integrability of C2-Cofinite Vertex Operator Algebras

【作者】 Chongying Dong 

【摘要】The following integrability theorem for vertex operator algebras V satisfying some finiteness conditions (C2-cofinite and CFT-type) is proved: the vertex operator subalgebra generated by a simple Lie subalgebra g of the weight one subspace V1 is isomorphic to the irreducible highest weight ?-module L(k; 0) for a positive integer k; and V is an integrable ?-module. The case in which g is replaced by an abelian Lie subalgebra is also considered; and several consequences of integrability are discussed. 2000MSC:17B69