On a quantum analog of the Grothendieck-Teichmueller group
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.
Keywords
Cite
@article{arxiv.math/0104275,
title = {On a quantum analog of the Grothendieck-Teichmueller group},
author = {Karl-Georg Schlesinger},
journal= {arXiv preprint arXiv:math/0104275},
year = {2009}
}
Comments
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