Construction and Classification of Holomorphic Vertex Operator Algebras

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.

37 pages, LaTeX; minor changes: numbering changed in Section 5, added results in Section 7, expanded Section 8; to appear in J. Reine Angew. Math. (Crelles Journal)

References in corpus (2)

• Orbifold construction of holomorphic vertex operator algebras associated to inner automorphisms
• A holomorphic vertex operator algebra of central charge $24$ whose weight one Lie algebra has type $A_{6,7}$

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