scholarly journals Computing fusion rules for spherical G-extensions of fusion categories

2021 ◽  
Vol 28 (2) ◽  
Author(s):  
Marcel Bischoff ◽  
Corey Jones
Keyword(s):  
Fusion Rules ◽  
Fusion Categories

scholarly journals On fusion rules and solvability of a fusion category

2017 ◽  
Vol 20 (1) ◽  
Author(s):  
Melisa Escañuela González ◽  
Sonia Natale
Keyword(s):  
Hopf Algebras ◽  
Fusion Category ◽  
Alternating Groups ◽  
Fusion Rules ◽  
Fusion Categories

AbstractWe address the question whether or not the condition on a fusion category being solvable is determined by its fusion rules. We prove that the answer is affirmative for some families of non-solvable examples arising from representations of semisimple Hopf algebras associated to exact factorizations of the symmetric and alternating groups. In the context of spherical fusion categories, we also consider the invariant provided by the

SOME NON-BRAIDED FUSION CATEGORIES OF RANK THREE

2009 ◽  
Vol 11 (04) ◽  
pp. 615-637 ◽  
Author(s):  
TOBIAS J. HAGGE ◽  
SEUNG-MOON HONG
Keyword(s):  
Simple Object ◽  
Fusion Rules ◽  
Graphical Calculus ◽  
Fusion Categories ◽  
Dual Functor

We classify all fusion categories for a given set of fusion rules with three simple object types. If a conjecture of Ostrik is true, our classification completes the classification of fusion categories with three simple object types. To facilitate the discussion, we describe a convenient, concrete and useful variation of graphical calculus for fusion categories, discuss pivotality and sphericity in this framework, and give a short and elementary re-proof of the fact that the quadruple dual functor is naturally isomorphic to the identity.

scholarly journals Fusion rules of equivariantizations of fusion categories

2013 ◽  
Vol 54 (1) ◽  
pp. 013511 ◽  
Author(s):  
Sebastian Burciu ◽  
Sonia Natale
Keyword(s):  
Fusion Rules ◽  
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

FUSION RULES FOR THE FRACTIONAL LEVEL $\widehat{{\rm sl}(2)}$ ALGEBRA

1992 ◽  
Vol 07 (13) ◽  
pp. 1185-1195 ◽  
Author(s):  
HIDETOSHI AWATA ◽  
YASUHIKO YAMADA
Keyword(s):  
Null Vector ◽  
Primary Field ◽  
Fusion Rules ◽  
Weyl Transformation ◽  
Interesting Structure

We derive, as the condition for the null vector decoupling, the fusion rules for the [Formula: see text] algebra with fractional level, which have an interesting structure related to affine Weyl transformation. It is shown that, to get non-trivial fusion rules, we must include the primary field which belongs to neither the highest nor the lowest weight representations.

scholarly journals Quantum dimensions and fusion rules of the VOA VLC×Dτ

2016 ◽  
Vol 459 ◽  
pp. 309-349 ◽  
Author(s):  
Hsian-Yang Chen ◽  
Ching Hung Lam
Keyword(s):  
Fusion Rules ◽  
Quantum Dimensions

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 Novel Fusion Rules for Discrete Wavelet Transformbased Image Fusion

2017 ◽  
Vol 10 (19) ◽  
pp. 1-6 ◽  
Author(s):  
Abhishek Sharma ◽  
Tarun Gulati ◽  
◽  
Keyword(s):  
Image Fusion ◽  
Discrete Wavelet ◽  
Fusion Rules
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