A spanning set for VOA modules

By G. Buhl. 2001

75 citations recorded by the source corpus.

We develop a spanning set for weak modules of C2 co-finite vertex operator algebras. This spanning set has certain finiteness properties that we use to show weak modules are Cn co-finite and An(M) is finite dimensional.

Subfields: Atomic and Molecular Physics, and Optics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/591d6b3987067ed0d87ef8f1ba215607e0dbdcf7

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Atomic and Molecular Physics, and Optics

1. Yi-Zhi Huang
2. Haisheng Li
3. C. Dong
4. T. Abe
5. Masahiko Miyamoto
6. Geoffrey Mason

In Geometry and Topology

1. Yi-Zhi Huang
2. T. Abe
3. Masahiko Miyamoto
4. Haisheng Li
5. T. Arakawa
6. C. Dong
7. Geoffrey Mason
8. T. Creutzig

In Mathematical Physics

1. Yi-Zhi Huang
2. Haisheng Li
3. T. Abe
4. C. Dong
5. Masahiko Miyamoto
6. Geoffrey Mason
7. T. Arakawa
8. T. Creutzig

Citations in the corpus

• Differential equations and intertwining operators (2002, methodology): “[DLM3], [L], [KarL], [GN], [ B ], [ABD] and [HKL].”
• Integrability of C2-cofinite vertex operator algebras (2006, background): “Interestingly, one of the basic features of C2-cofinite vertex operator algebras, namely that they possess a PBW-type spanning set with the nonrepeat condition ([GN], [ B ], [ABD]), was not discovered until several years after the publication of Zhu’s paper.”
• Rationality, regularity, and ₂-cofiniteness (2003, unknown): “Proof. First, we must look back to the proof of Theorem 3.3 [ 4 ].”
• Abelianizing Vertex Algebras (2004, methodology): “Furthermore, for any N-graded vertex algebra V = n∈N V(n) with V(0) = C1, we constructed a canonical good increasing filtration of V . This increasing filtration was essentially used in [KL, GN, Bu1 , 2, ABD and NT] in the study on generating subspaces of V with a certain property analogous to the ”
• Modular invariance of vertex operator algebras satisfying $C_{2}$-cofiniteness (2002, background): “s U, the maximal weak V-submodule D(U) of Hom(U,C) introduced in [Li2] is an N-graded weak module. The most results about C2-cofininteness came from the existence of some spanning set, e.g. [GN],[Li2],[Bu],[ABD], We will prove the existence of the following spanning set for a general VOA without nega”
• Rationality, Regularity, and C_2-cofiniteness (2002, methodology): “The PBW type spanning set for weak modules obtained in [4] is the key for us to obtain a lowest weight vector.”