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arXiv · 1609.02321

Quantum groups based on spatial partitions

Guillaume Cébron·Moritz Weber
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Abstract

We define new compact matrix quantum groups whose intertwiner spaces are dual to tensor categories of three-dimensional set partitions -- which we call spatial partitions. This extends substantially Banica and Speicher's approach of the so called easy quantum groups: It enables us to find new examples of quantum subgroups of Wang's free orthogonal quantum group $O_n^+$ which do not contain the symmetric group $S_n$; we may define new kinds of products of quantum groups coming from new products of categories of partitions; and we give a quantum group interpretation of certain categories of partitions which do neither contain the pair partition nor the identity partition.

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Guillaume Cébron, Moritz Weber. 2016-09-08. Quantum groups based on spatial partitions. https://arxiv.org/abs/1609.02321

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