Arveson, William

The free cover of a row contraction

Doc. Math., J. DMV 9, 137-161 (2004)

Summary

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.

Mathematics Subject Classification

46L07, 47A99

Keywords/Phrases

free resolutions, multivariable operator theory

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