Geodesic
The free cover of a row contraction
Documenta mathematica, Tome 9 (2004), pp. 137-161
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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.
DOI : 10.4171/dm/162
Classification : 46L07, 47A99
Mots-clés : free resolutions, multivariable operator theory 
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     author = {William Arveson},
     title = {The free cover of a row contraction},
     journal = {Documenta mathematica},
     pages = {137--161},
     year = {2004},
     volume = {9},
     doi = {10.4171/dm/162},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/162/}
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William Arveson. The free cover of a row contraction. Documenta mathematica, Tome 9 (2004), pp. 137-161. doi: 10.4171/dm/162

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