Rational series in the free group and the Connes operator
classification
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math.GR
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rationalfreeseriesconnesgroupoperatoralgorithmcharacterize
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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.
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