A theory of tensor products for vertex operator algebra satsifying C_2-cofiniteness
| dc.creator | Miyamoto, Masahiko | |
| dc.date | 2003-09-22 | |
| dc.date | 2003-12-02 | |
| dc.date.accessioned | 2026-07-07T05:01:20Z | |
| dc.date.available | 2026-07-07T05:01:20Z | |
| dc.description | 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 C_2-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 particular, we don't assume the semisimplicity of the weight operator L(0). Actually, without the assumption of rationality, a C_2-cofiniteness on V is enough to obtain the existence of a tensor product of two Artin modules and natural associativity of tensor products. Namely, the category of Artin modules becomes a braided tensor category. As an application of the tensor product theory under C_2-cofiniteness, we proved the rationality of some orbifold models. For example, if a vertex operator algebra V has a finite automorphism group and the fixed point vertex operator subalgebra V^G is C_2-cofinite, then for any irreducible V^{<g>}-module W, there is an element h\in <g> such that W is contained in some h-twisted V-module. Furthermore, if V^G is rational, then V^{<g>} is also rational for any g\in G. | |
| dc.description | 27 pages. Latex | |
| dc.identifier | https://arxiv.org/abs/math/0309350 | |
| dc.identifier | http://arxiv.org/abs/math/0309350 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/68634 | |
| dc.subject | Quantum Algebra | |
| dc.title | A theory of tensor products for vertex operator algebra satsifying C_2-cofiniteness | |
| dc.type | text |