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Construction and Classification of Holomorphic Vertex Operator Algebras (1507.08142v3)
Published 29 Jul 2015 in math.RT and math.QA
Abstract: We develop an orbifold theory for finite, cyclic groups acting on holomorphic vertex operator algebras. Then we show that Schellekens' classification of $V_1$-structures of meromorphic conformal field theories of central charge 24 is a theorem on vertex operator algebras. Finally we use these results to construct some new holomorphic vertex operator algebras of central charge 24 as lattice orbifolds.