Quantized representations of knot groups
Abstract
We propose a new non-commutative generalization of the representation variety and the character variety of a knot group. Our strategy is to reformulate the construction of the algebra of functions on the space of representations in terms of Hopf algebra objects in a braided category (braided Hopf algebra). The construction works under the assumption that the algebra is braided commutative. The resulting knot invariant is a module with a coadjoint action. Taking the coinvariants yields a new quantum character variety that may be thought of as an alternative to the skein module. We give concrete examples for a few of the simplest knots and links.
Keywords
Cite
@article{arxiv.1812.09539,
title = {Quantized representations of knot groups},
author = {Jun Murakami and Roland van der Veen},
journal= {arXiv preprint arXiv:1812.09539},
year = {2022}
}
Comments
28 pages, abstract and introduction are revised, title is changed and the main theorem, its proof and examples are reformulated