Rationality of vertex operator algebra V L + : higher rank
نویسندگان
چکیده
منابع مشابه
Rationality of the vertex algebra V + L when L is a nondegenerate even lattice of arbitrary rank
In this paper we prove that the vertex algebra V + L is rational if L is a negative definite even lattice of finite rank , or if L is a non-degenerate even lattice of a finite rank that is neither positive definite nor negative definite. In particular, for such even lattices L, we show that the Zhu algebras of the vertex algebras V + L are semisimple. This extends the result of Abe from [A2] wh...
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It is shown that any simple, rational and C2-cofinite vertex operator algebra whose weight 1 subspace is zero, the dimension of weight 2 subspace is greater than or equal to 2 and with central charge c = 1, is isomorphic to L(12 , 0) ⊗ L( 1 2 , 0). 2000MSC:17B69
متن کاملRationality of vertex operator algebras
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.
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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 کاملThe rank two lattice type vertex operator algebras V + L and their automorphism groups
Let L be a positive definite even lattice and V + L be the fixed points of the lattice VOA VL associated to L under an automorphism of VL lifting the −1 isometry of L. For any positive rank, the full automorphism group of V + L is determined if L does not have vectors of norms 2 or 4. For any L of rank 2, a set of generators and the full automorphism group of V + L are determined. 1991 Mathemat...
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ژورنال
عنوان ژورنال: Proceedings of the London Mathematical Society
سال: 2012
ISSN: 0024-6115
DOI: 10.1112/plms/pdr055