Classification of Globally Colorized Categories of Partitions

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.

arXiv comment25 pages

References in corpus (2)

• Liberation of orthogonal Lie groups
• The combinatorics of an algebraic class of easy quantum groups

Cited by in corpus (3)

• Generating linear categories of partitions
• New products and ${\mathbb{Z}}_2$-extensions of compact matrix quantum groups
• Gluing compact matrix quantum groups