Rational series in the free group and the Connes operator
Combinatorics
2018-06-12 v1 Group Theory
Abstract
We characterize rational series over the free group by using an operator introduced by A. Connes. We prove that rational Malcev--Neumann series posses rational expressions without simplifications. Finally, we develop an effective algorithm for solving the word problem in the free skew field.
Cite
@article{arxiv.1806.03540,
title = {Rational series in the free group and the Connes operator},
author = {Aaron Lauve and Christophe Reutenauer},
journal= {arXiv preprint arXiv:1806.03540},
year = {2018}
}
Comments
22 pages, 2 figures