Article ID Journal Published Year Pages File Type
4596213 Journal of Pure and Applied Algebra 2014 13 Pages PDF
Abstract

We define the notion of a (linearly reductive) center for a linearly reductive quantum group, and show that the quotient of a such a quantum group by its center is simple whenever its fusion semiring is free in the sense of Banica and Vergnioux. We also prove that the same is true of free products of quantum groups under very mild non-degeneracy conditions. Several natural families of compact quantum groups, some with non-commutative fusion semirings and hence very “far from classical”, are thus seen to be simple. Examples include quotients of free unitary groups by their centers, recovering previous work, as well as quotients of quantum reflection groups by their centers.

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Related Topics
Physical Sciences and Engineering Mathematics Algebra and Number Theory
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