On a quantum analog of the Grothendieck-Teichmueller group

Details On a quantum analog of the Grothendieck-Teichmueller group On a quantum analog of the Grothendieck-Teichmueller group

2001-04-28

arxiv.org/abs/math/0104275v3

Mathematics

Quantum Algebra

12 pages, changes in second version: An additional section on the explicit calculation of the elements of the quantum analog h

Scientific paper

10.1088/0305-4470/35/47/315

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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