# Un critère de rationalité provenant de la géométrie non commutative

@article{Duchamp1997UnCD,
title={Un crit{\e}re de rationalit{\'e} provenant de la g{\'e}om{\'e}trie non commutative},
author={G{\'e}rard Duchamp and Christophe Reutenauer},
journal={Inventiones mathematicae},
year={1997},
volume={128},
pages={613-622}
}`
• Published 1 September 1997
• Mathematics
• Inventiones mathematicae
We prove a conjecture of A. Connes, which gives a rationality criterion for elements of the closure of ℂΓ (Γ a free group) in the space of bounded operators in l2(Γ). We show that this criterion applies also to the ring of Malcev-Neumann series on Γ.
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