Generating linear categories of partitions

Abstract

We present an algorithm for approximating linear categories of partitions (of sets). We report on concrete computer experiments based on this algorithm which we used to obtain first examples of so-called non-easy linear categories of partitions. All of the examples that we constructed are proven to be indeed new and non-easy. We interpret some of the new categories in terms of quantum group anticommutative twists.

arXiv comment41 pages; reformulated Sect. 4, added Sect. 6

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Cited by in corpus (5)

• Some examples of quantum graphs
• Quantum symmetries of Cayley graphs of abelian groups
• Semisimplicity and Indecomposable Objects in Interpolating Partition Categories
• Free quantum analogue of Coxeter group $D_4$
• Presentations of projective quantum groups