Rational Vertex Operator Algebras and the Effective Central Charge

Details Rational Vertex Operator Algebras and the Effective Central Charge Rational Vertex Operator Algebras and the Effective Central Charge

2002-01-31

arxiv.org/abs/math/0201318v1

Mathematics

Quantum Algebra

latex 18 pages

Scientific paper

We establish that the Lie algebra of weight one states in a (strongly) rational vertex operator algebra is reductive, and that its Lie rank is bounded above by the effective central charge. We show that lattice vertex operator algebras may be characterized by the equalities of the effective central charge, the Lie rank and the central charge, and in particular holomorphic lattice theories may be characterized among all holomorphic vertex operator algebras by the equality of the Lie rank and the central charge.

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