We analyse perturbative expansions of the invariants defined from unitary representations of the Quantum Lorentz Group in two different ways, namely using the Kontsevich Integral and weight systems, and the R-matrix in the Quantum Lorentz Group defined by Buffenoir and Roche. The two formulations are proved to be equivalent; and they both yield ℂ[[h]]h-valued knot invariants related with the Melvin-Morton expansion of the Coloured Jones Polynomial.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm188-0-4,
author = {Jo\~ao Faria Martins},
title = {Knot theory with the Lorentz group},
journal = {Fundamenta Mathematicae},
volume = {185},
year = {2005},
pages = {59-93},
zbl = {1106.57010},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm188-0-4}
}
João Faria Martins. Knot theory with the Lorentz group. Fundamenta Mathematicae, Tome 185 (2005) pp. 59-93. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm188-0-4/