Alphabeta MathZhu Rationality And Modular Interfaces
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1 · Prerequisites
Abstract Algebra
Combinatorics
Lie Theory
Linear Algebra
Quantum Algebra and Representation Theory
Quantum Field Theory Mathematics
Real Analysis
2 · Logical flowchart
3 · Items
Definition
Higher Zhu quotients and candidate products
Definition
Regularity of a vertex operator algebra
Lemma
A simple ordinary module admits a nonnegative grading
Theorem
Associative structure of the higher Zhu quotients
Theorem
Zhu quotient algebra and admissible top-level action
Lemma
Higher Zhu action on the Omega spaces of an arbitrary weak module
Definition
Strongly rational VOA convention
Lemma
Zhu top induction, simple correspondence, and forward rationality
Lemma
Finite mode windows for a nonnegative C2-cofinite VOA
Sources
- Chongying Dong, Haisheng Li, and Geoffrey Mason, Vertex operator algebras and associative algebras
- Abe, Buhl, and Dong, Rationality, regularity, and C2-cofiniteness
- Chongying Dong and Cuipo Jiang, Rationality of Vertex Operator Algebras
- Tomoyuki Arakawa and Anne Moreau, Arc spaces and vertex algebras
- Dong, Li and Mason, Vertex operator algebras and associative algebras
- Yi-Zhi Huang, Rigidity and modularity of vertex tensor categories
- Shun Xu, G-crossed braided tensor categories of twisted modules
- Dong, Li, and Mason, Vertex operator algebras and associative algebras
- Dong and Jiang, Rationality of vertex operator algebras
- Miyamoto, Modular invariance of vertex operator algebras satisfying C2-cofiniteness