Osaka Journal of Mathematics

A category of spectral triples and discrete groups with length function

Paolo Bertozzini, Roberto Conti, and Wicharn Lewkeeratiyutkul

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In the context of Connes' spectral triples, a suitable notion of morphism is introduced. Discrete groups with length function provide a natural example for our definitions. Connes' construction of spectral triples for group algebras is a covariant functor from the category of discrete groups with length functions to that of spectral triples. Several interesting lines for future study of the categorical properties of spectral triples and their variants are suggested.

Article information

Osaka J. Math., Volume 43, Number 2 (2006), 327-350.

First available in Project Euclid: 6 July 2006

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Zentralblatt MATH identifier

Primary: 46L87: Noncommutative differential geometry [See also 58B32, 58B34, 58J22]
Secondary: 18F99: None of the above, but in this section 20C07: Group rings of infinite groups and their modules [See also 16S34] 22D15: Group algebras of locally compact groups


Bertozzini, Paolo; Conti, Roberto; Lewkeeratiyutkul, Wicharn. A category of spectral triples and discrete groups with length function. Osaka J. Math. 43 (2006), no. 2, 327--350.

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