On a quantum analog of the Grothendieck-Teichmueller group
arXiv:math/0104275 · doi:10.1088/0305-4470/35/47/315
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.
12 pages, changes in second version: An additional section on the explicit calculation of the elements of the quantum analog has been added. Changes in the third version: Calculations and proofs are given in more deatil. accepted for J. Phys. A