Rational series in the free group and the Connes operator
Aaron Lauve, Christophe Reutenauer · Contemporary mathematics - American Mathematical Society · 2013
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.