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arXiv · 1805.10800

Classification of Globally Colorized Categories of Partitions

Daniel Gromada
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Abstract

Set partitions closed under certain operations form a tensor category. They give rise to certain subgroups of the free orthogonal quantum group $O_n^+$, the so called easy quantum groups, introduced by Banica and Speicher in 2009. This correspondence was generalized to two-colored set partitions, which, in addition, assign a black or white color to each point of a set. Globally colorized categories of partitions are those categories that are invariant with respect to arbitrary permutations of colors. This article presents a classification of globally colorized categories. In addition, we show that the corresponding unitary quantum groups can be constructed from the orthogonal ones using tensor complexification.

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Daniel Gromada. 2018-05-28. Classification of Globally Colorized Categories of Partitions. https://doi.org/10.1142/s0219025718500297

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