# Associators with Frozen Feet

## The Goal

The purpose of the paperlet is to find an explicit formula for an associator with frozen feet. As I'm starting to write, I don't know such a formula. My hope is that as I type up all the relevant equations, a solution will emerge. I'll be just as happy if it emerges in somebody else's mind, provided (s)he shares her/his thoughts.

An **associator** is a solution of the pentagon equation and the hexagon equations ([Drinfeld_90], [Drinfeld_91], [Bar-Natan_97]):

[Pentagon] |

[Hexagons] |

## References

[Bar-Natan_97] **^** D. Bar-Natan, *Non-associative tangles,* in *Geometric topology* (proceedings of the Georgia international topology conference), (W. H. Kazez, ed.), 139-183, Amer. Math. Soc. and International Press, Providence, 1997.

[Drinfeld_90] **^** V. G. Drinfel'd, *Quasi-Hopf algebras,* Leningrad Math. J. **1** (1990) 1419-1457.

[Drinfeld_91] **^** V. G. Drinfel'd, *On quasitriangular Quasi-Hopf algebras and a group closely connected with ,* Leningrad Math. J. **2** (1991) 829-860.