Data

Tools

Indexes

Applications

Experiments

Open Source Science

f-symbols-double-haagerup

Explicit solutions for the F- and R-symbols for the Drinfeld double of the Haagerup fusion category. Computed with the Julia package TensorCategories.jl

https://github.com/fabianmaeurer/f-symbols-double-haagerup

Science Score: 36.0%

This score indicates how likely this project is to be science-related based on various indicators:

  • ○
    CITATION.cff file
  • ✓
    codemeta.json file
    Found codemeta.json file
  • ✓
    .zenodo.json file
    Found .zenodo.json file
  • ○
    DOI references
  • ✓
    Academic publication links
    Links to: arxiv.org
  • ○
    Academic email domains
  • ○
    Institutional organization owner
  • ○
    JOSS paper metadata
  • ○
    Scientific vocabulary similarity
    Low similarity (3.6%) to scientific vocabulary
Last synced: 10 months ago · JSON representation

Repository

Explicit solutions for the F- and R-symbols for the Drinfeld double of the Haagerup fusion category. Computed with the Julia package TensorCategories.jl

Basic Info
  • Host: GitHub
  • Owner: FabianMaeurer
  • License: mit
  • Default Branch: main
  • Size: 1.46 GB
Statistics
  • Stars: 0
  • Watchers: 0
  • Forks: 0
  • Open Issues: 0
  • Releases: 0
Created 11 months ago · Last pushed 11 months ago
Metadata Files
Readme License Citation

README.md

F-Symbols for the Double of the Haagerup fusion category

Using the Julia Package TensorCategories.jl we where able to compute the $F$- ans $R$-symbols of the drinfeld double of the fusion category $\mathcal H3$ comming from the Haagerup subfactor. To accomplish this we used the F-symbols for $\mathcal H3$ computed for the Anyonwiki and fed that to the algorithm we developed in [1].

The Data

We provid the data in algebraic and numeric form. The solutions in the folders "DoubleHaagerup#Symbols" are formatted as a csv where the first ten columns $a,b,c,d,f,\gamma,\delta,e,\beta,\alpha$ correspond to the index of the $F$-symbol ```math \left[F{a,b,c}^d\right]_{f, \delta,\gamma}^{e,\alpha, \beta} ``` are either algerbaic numbers or numeric symbols depending on the folder. The numeric ones are self-explanatory.

Algebraic Data

The algebraic solutions in the folder "AlgebraicSymbols/DoubleHaagerup#_Symbols" are formatted such that they show a 48-dimensional vector correspponding to the coefficients the standard basis $1,x,...,x^{47}$ of the Numberfield math K = \mathbb Q(x), ~~~ 0 = x^{48} - x^{47} + 2x^{46} - 2x^{45} + 2x^{44} - x^{43} - x^{42} + 4x^{41} - 8x^{40} + 12x^{39} - 15x^{38} + 15x^{37} - 10x^{36} + 51x^{35} - 31x^{34} + 57x^{33} - 27x^{32} + 2x^{31} + 59x^{30} - 141x^{29} + 229x^{28} - 313x^{27} + 342x^{26} - 285x^{25} + 85x^{24} + 285x^{23} + 342x^{22} + 313x^{21} + 229x^{20} + 141x^{19} + 59x^{18} - 2x^{17} - 27x^{16} - 57x^{15} - 31x^{14} - 51x^{13} - 10x^{12} - 15x^{11} - 15x^{10} - 12x^{9} - 8x^{8} - 4x^{7} - x^{6} + x^{5} + 2x^{4} + 2x^{3} + 2x^{2} + x + 1

In TensorCategories.jl

The data is also available in the Julia package TensorCategories.jl where they were computed.

```julia julia> using TensorCategories

julia> C = haagerupH3center() Center of fusion category HI(Z3) ```

[1] F. Murer, U. Thiel, "Computing the center of a fusion category", https://arxiv.org/abs/2406.13438

Owner

  • Login: FabianMaeurer
  • Kind: user

GitHub Events

Total
  • Push event: 1
Last Year
  • Push event: 1