Braided Tensor Categories and Extensions of Vertex Operator Algebras

By Yi-Zhi Huang, A. Kirillov, James Lepowsky. 2014

190 citations recorded by the source corpus.

Let V be a vertex operator algebra satisfying suitable conditions such that in particular its module category has a natural vertex tensor category structure, and consequently, a natural braided tensor category structure. We prove that the notions of extension (i.e., enlargement) of V and of commutative associative algebra, with uniqueness of unit and with trivial twist, in the braided tensor category of V-modules are equivalent.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/2b0165366c409861bcea3ff8573316236b082b4b

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In Algebra and Number Theory

1. T. Creutzig
2. A. Linshaw
3. Shashank Kanade

In Geometry and Topology

1. T. Creutzig
2. Shashank Kanade
3. A. Linshaw

In Mathematical Physics

1. T. Creutzig
2. A. Linshaw

Citations in the corpus

• Fusion categories for affine vertex algebras at admissible levels (2018, methodology): “This theory uses that vertex algebra extensions are in one-to-one correspondence to commutative, associative, haploid algebras in the vertex tensor category [17, 18, 19].”
• Simple current extensions beyond semi-simplicity (2015, background): “ading, we immediately conclude that Ye(u,x)vmust have only integral powers of x. Skew-symmetry with the correct factor of −1, vacuum property, creation property and associativity follow exactly as in [HKL]. Using [H2], skew-symmetry and the associativity imply the right kind of commutativity for a v”