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Un critère de rationalité provenant de la géométrie non commutative

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Abstract

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 l 2(Γ). We show that this criterion applies also to the ring of Malcev-Neumann series on Γ.

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Oblatum 2-VIIM996 ⇐p; 20-IX-1996

À la mémoire de M. P. Schützenberger

Soutenu par le GDR AMI.

L’auteur a bénéficié d’une subvention CRSNG (Canada) et de l’hospitalité de l’Université Louis Pasteur (Strasbourg).

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Duchamp, G., Reutenauer, C. Un critère de rationalité provenant de la géométrie non commutative. Invent. math. 128, 613–622 (1997). https://doi.org/10.1007/s002220050154

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  • DOI: https://doi.org/10.1007/s002220050154

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