English

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