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5 papers · 1 filter
Hopf quivers and Nichols algebras in positive characteristic
Claude Cibils, Aaron Lauve, Sarah Witherspoon
We apply a combinatorial formula of the first author and Rosso, for products in Hopf quiver algebras, to determine the structure of Nichols algebras. We illustrate this technique b…
Categorical centers and Reshetikhin-Turaev invariants
Alain Bruguières, Alexis Virelizier
The center Z(C) of a spherical fusion category C (over an arbitrary commutative ring) is modular. We give an algorithm for computing the Reshetikhin-Turaev invariant defined with Z…
The invariant of Turaev-Viro from Group category
Jerome Petit
A Group category is a spherical category whose simple objects are invertible. The invariant of Turaev-Viro with this particular category is in fact the invariant of Dijkgraaf-Witte…
N-complexes as functors, amplitude cohomology and fusion rules
Claude Cibils, Andrea Solotar, Robert Wisbauer
We consider N-complexes as functors over an appropriate linear category in order to show first that the Krull-Schmidt Theorem holds, then to prove that amplitude cohomology only va…
Double Braidings, Twists, and Tangle Invariants
Alain Bruguières
A tortile (or ribbon) category defines invariants of ribbon (framed) links and tangles. We observe that these invariants, when restricted to links, string links, and more general t…