scholarly journals Lie theory for fusion categories: A research primer

Author(s):  
Andrew Schopieray
Keyword(s):  
2014 ◽  
Vol 23 (4) ◽  
pp. 591-608 ◽  
Author(s):  
A. Bruguières ◽  
Sebastian Burciu

2005 ◽  
Vol 38 (2) ◽  
pp. 303-338 ◽  
Author(s):  
A ALEKSEEV ◽  
E MEINRENKEN
Keyword(s):  

2013 ◽  
Vol 24 (01) ◽  
pp. 1250126 ◽  
Author(s):  
SEUNG-MOON HONG

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.


2001 ◽  
Vol 43 (1) ◽  
pp. 1
Author(s):  
U. Helmke ◽  
K. Hüper ◽  
J. Lawson
Keyword(s):  

2017 ◽  
Vol 28 (01) ◽  
pp. 1750009 ◽  
Author(s):  
Scott Morrison ◽  
Kevin Walker

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 .


2013 ◽  
Vol 22 (1) ◽  
pp. 229-240 ◽  
Author(s):  
Sonia Natale ◽  
Julia Yael Plavnik
Keyword(s):  

1974 ◽  
Vol 15 (8) ◽  
pp. 1263-1274 ◽  
Author(s):  
E. G. Kalnins ◽  
Willard Miller

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