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On a quantum analog of the Grothendieck-Teichmueller group

Karl-Georg Schlesinger
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Abstract

We introduce a noncommutative and noncocommutative Hopf algebra which takes for certain Hopf categories (and therefore braided monoidal bicategories) a similar role as the Grothendieck- Teichmueller group for quasitensor categories. We also give a result which highly restricts the possibility for similar structures for even higher weak n-categories than bicategories by showing that these structures would not allow for any nontrivial deformations. Finally, we give an explicit description of the elements of this Hopf algebra.

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Karl-Georg Schlesinger. 2002-12-21. On a quantum analog of the Grothendieck-Teichmueller group. https://doi.org/10.1088/0305-4470%2F35%2F47%2F315

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