Rationality of vertex operator algebras
نویسنده
چکیده
It is shown that a simple vertex operator algebra V is rational if and only if its Zhu algebra A(V ) is semisimple and each irreducible admissible V -module is ordinary. A contravariant form on a Verma type admissible V -module is constructed and the radical is exactly the maximal proper submodule. As an application the rationality of V + L for any positive definite even lattice is obtained.
منابع مشابه
Representations of vertex operator algebras
This paper is an exposition of the representation theory of vertex operator algebras in terms of associative algebras An(V ) and their bimodules. A new result on the rationality is given. That is, a simple vertex operator algebra V is rational if and only if its Zhu algebra A(V ) is a semisimple associative algebra. 2000MSC:17B69
متن کاملSimple currents and extensions of vertex operator algebras
We consider how a vertex operator algebra can be extended to an abelian intertwining algebra by a family of weak twisted modules which are simple currents associated with semisimple weight one primary vectors. In the case that the extension is again a vertex operator algebra, the rationality of the extended algebra is discussed. These results are applied to affine Kac-Moody algebras in order to...
متن کاملGeneralized Rationality and a “Jacobi Identity” for Intertwining Operator Algebras
We prove a generalized rationality property and a new identity that we call the “Jacobi identity” for intertwining operator algebras. Most of the main properties of genus-zero conformal field theories, including the main properties of vertex operator algebras, modules, intertwining operators, Verlinde algebras, and fusing and braiding matrices, are incorporated into this identity. Together with...
متن کاملA theory of tensor products for vertex operator algebra satisfying C
We reformed the tensor product theory of vertex operator algebras developed by Huang and Lepowsky so that we could apply it to all vertex operator algebras satisfying C2-cofiniteness. We also showed that the tensor product theory develops naturally if we include not only ordinary modules, but also weak modules with a composition series of finite length (we call it an Artin module). In particula...
متن کاملRationality of Virasoro Vertex Operator Algebras
Vertex operator algebras (VOA) were introduced by Borcherds ( [B] ) as an axiomatic description of the ‘holomorphic part’ of a conformal field theory ( [BPZ] ). An account of the theory of vertex operator algebras may be found in [FLM]. One of the most important examples of VOAs ( [FZ] ) is the Virasoro VOAs, i.e.VOAs corresponding to the representations of the Virasoro algebra L, denoted by Vc...
متن کاملFixed point subalgebras of lattice vertex operator algebras by an automorphism of order three
We study the fixed point subalgebra of a certain class of lattice vertex operator algebras by an automorphism of order 3, which is a lift of a fixed-point-free isometry of the underlying lattice. We classify the irreducible modules for the subalgebra. Moreover, the rationality and the C2-cofiniteness of the subalgebra are established. Our result contains the case of the vertex operator algebra ...
متن کامل