Rational Vertex Operator Algebras and the Effective Central Charge
نویسنده
چکیده
We establish that the Lie algebra of weight one states in a (strongly) rational vertex operator algebra is reductive, and that its Lie rank l is bounded above by the effective central charge c̃. We show that lattice vertex operator algebras may be characterized by the equalities c̃ = l = c, and in particular holomorphic lattice theories may be characterized among all holomorphic vertex operator algebras by the equality l = c.
منابع مشابه
Framed vertex operator algebras, codes and the moonshine module
For a simple vertex operator algebra whose Virasoro element is a sum of commutative Virasoro elements of central charge 1 2 , two codes are introduced and studied. It is proved that such vertex operator algebras are rational. For lattice vertex operator algebras and related ones, decompositions into direct sums of irreducible modules for the product of the Virasoro algebras of central charge 1 ...
متن کاملToward classfication of rational vertex operator algebras with central charges less than 1
The rational and C2-cofinite simple vertex operator algebras whose effective central charges and the central charges c are equal and less than 1 are classified. Such a vertex operator algebra is zero if c̃ < 0 and C if c̃ = 0. If c̃ > 0, it is an extension of discrete Virasoro vertex operator algebra L(cp,q, 0) by its irreducible modules. It is also proved that for any rational and C2-cofinite sim...
متن کاملZ 3 Symmetry and W 3 Algebra in Lattice Vertex Operator Algebras
The vertex operator algebras associated with positive definite even lattices afford a large family of known examples of vertex operator algebras. An isometry of the lattice induces an automorphism of the lattice vertex operator algebra. The subalgebra of fixed points of an automorphism is the so-called orbifold vertex operator algebra. In this paper we deal with the case where the lattice L = √...
متن کاملDeformation of central charges, vertex operator algebras whose Griess algebras are Jordan algebras
If a vertex operator algebra V = ⊕n=0Vn satisfies dimV0 = 1, V1 = 0, then V2 has a commutative (nonassociative) algebra structure called Griess algebra. One of the typical examples of commutative (nonassociative) algebras is a Jordan algebra. For example, the set Symd(C) of symmetric matrices of degree d becomes a Jordan algebra. On the other hand, in the theory of vertex operator algebras, cen...
متن کاملHolomorphic Vertex Operator Algebras of Small Central Charge
We provide a rigorous mathematical foundation to the study of strongly rational, holomorphic vertex operator algebras V of central charge c = 8, 16 and 24 initiated by Schellekens. If c = 8 or 16 we show that V is isomorphic to a lattice theory corresponding to a rank c even, self-dual lattice. If c = 24 we prove, among other things, that either V is isomorphic to a lattice theory corresponding...
متن کامل