scholarly journals Fusion categories for affine vertex algebras at admissible levels

2019 ◽  
Vol 25 (2) ◽  
Author(s):  
Thomas Creutzig
Keyword(s):  
Vertex Algebras ◽  
Fusion Categories

scholarly journals On Normal Tensor Functors and Coset Decompositions for Fusion Categories

2014 ◽  
Vol 23 (4) ◽  
pp. 591-608 ◽  
Author(s):  
A. Bruguières ◽  
Sebastian Burciu
Keyword(s):  
Fusion Categories ◽  
Normal Tensor

scholarly journals Associating quantum vertex algebras to Lie algebragl∞

2014 ◽  
Vol 399 ◽  
pp. 1086-1106 ◽  
Author(s):  
Cuipo Jiang ◽  
Haisheng Li
Keyword(s):  
Vertex Algebras ◽  
Quantum Vertex

scholarly journals FROM RIBBON CATEGORIES TO GENERALIZED YANG–BAXTER OPERATORS AND LINK INVARIANTS (AFTER KITAEV AND WANG)

2013 ◽  
Vol 24 (01) ◽  
pp. 1250126 ◽  
Author(s):  
SEUNG-MOON HONG
Keyword(s):  
The Other ◽  
Polynomial Invariant ◽  
Link Invariants ◽  
Fusion Categories ◽  
New Family ◽  
Kauffman Polynomial ◽  
Twist Structure

We consider two approaches to isotopy invariants of oriented links: one from ribbon categories and the other from generalized Yang–Baxter (gYB) operators with appropriate enhancements. The gYB-operators we consider are obtained from so-called gYBE objects following a procedure of Kitaev and Wang. We show that the enhancement of these gYB-operators is canonically related to the twist structure in ribbon categories from which the operators are produced. If a gYB-operator is obtained from a ribbon category, it is reasonable to expect that two approaches would result in the same invariant. We prove that indeed the two link invariants are the same after normalizations. As examples, we study a new family of gYB-operators which is obtained from the ribbon fusion categories SO (N)2, where N is an odd integer. These operators are given by 8 × 8 matrices with the parameter N and the link invariants are specializations of the two-variable Kauffman polynomial invariant F.

scholarly journals A universal approach to vertex algebras

2010 ◽  
Vol 324 (7) ◽  
pp. 1731-1753 ◽  
Author(s):  
Ruthi Hortsch ◽  
Igor Kriz ◽  
Aleš Pultr
Keyword(s):  
Vertex Algebras ◽  
Universal Approach

scholarly journals The center of the extended Haagerup subfactor has 22 simple objects

2017 ◽  
Vol 28 (01) ◽  
pp. 1750009 ◽  
Author(s):  
Scott Morrison ◽  
Kevin Walker
Keyword(s):  
Fusion Category ◽  
Dimension Function ◽  
Fusion Ring ◽  
Fusion Categories ◽  
Modular Data ◽  
Grothendieck Rings ◽  
Combinatorial Data

We explain a technique for discovering the number of simple objects in [Formula: see text], the center of a fusion category [Formula: see text], as well as the combinatorial data of the induction and restriction functors at the level of Grothendieck rings. The only input is the fusion ring [Formula: see text] and the dimension function [Formula: see text]. In particular, we apply this to deduce that the center of the extended Haagerup subfactor has 22 simple objects, along with their decompositions as objects in either of the fusion categories associated to the subfactor. This information has been used subsequently in [T. Gannon and S. Morrison, Modular data for the extended Haagerup subfactor (2016), arXiv:1606.07165 .] to compute the full modular data. This is the published version of arXiv:1404.3955 .

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