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arXiv:1806.03540 [math.CO]AbstractReferencesReviewsResources

Rational series in the free group and the Connes operator

Aaron Lauve, Christophe Reutenauer

Published 2018-06-09Version 1

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.

Comments: 22 pages, 2 figures
Journal: Noncommutative birational geometry, representations and combinatorics, pp. 177-197, Contemp. Math., v. 592, Amer. Math. Soc., Providence, RI, 2013
Categories: math.CO, math.GR
Subjects: 20E05, 03D05, 13F25, 16S10
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