Alphabeta MathHow statement and proof provenance work
The first chip identifies the source of the statement or construction; the second identifies the source of its local proof or verification.
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Fusion rules
Definition
For a multifusion category choose a finite supplied list of representatives of its simple isomorphism classes. The fusion rules are the nonnegative integers determined by
in . Jordan--Hölder makes the multiplicities independent of a chosen composition series.
Depends on
Used by
- Fixed-boundary anyonic fusion-path space Definition
- Tensor-invertible objects, fusion-ring units, and invertible operators Definition
- Fusion rules for a supplied finite simple family Example
- Balancing and the Hopf-link character identity Lemma
- Distinct fusion-ring characters are orthogonal under duality Lemma
- Fusion paths give a basis of the fixed-boundary path space Lemma
- Modular Gauss sums, the Kirby color, and its slide identity Lemma
- The Fibonacci ring class is a unit but its simple object is not tensor-invertible Proposition
Dependency tree · two levels
10 results within two dependency steps of this one, each drawn at its shortest distance from it. An arrow runs from a result to what uses it, so the chart reads left to right and ends at this result, which carries a heavier outline. Every node is a link to that result. Click elsewhere on the chart to enlarge it.
Sources
- Etingof, Gelaki, Nikshych, Ostrik, Tensor Categories, Remark 4.5.3 (standard reference, not scraped)