Geodesic
The free cover of a row contraction
Documenta mathematica, Tome 9 (2004), pp. 137-161.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: We establish the existence and uniqueness of finite free resolutions - and their attendant Betti numbers - for graded commuting $d$-tuples of Hilbert space operators. Our approach is based on the notion of free cover of a (perhaps noncommutative) row contraction. Free covers provide a flexible replacement for minimal dilations that is better suited for higher-dimensional operator theory.
Classification : 46L07, 47A99
Keywords: free resolutions, multivariable operator theory 
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     author = {Arveson, William},
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Arveson, William. The free cover of a row contraction. Documenta mathematica, Tome 9 (2004), pp. 137-161. http://geodesic.mathdoc.fr/item/DOCMA_2004__9__a20/