A Category of Spectral Triples and Discrete Groups with Length Function

Details A Category of Spectral Triples and Discrete Groups with Length Function A Category of Spectral Triples and Discrete Groups with Length Function

2005-02-28

arxiv.org/abs/math/0502583v1

Osaka Journal of Mathematics, 43 n. 2, 327-350 (2006)

Mathematics

Operator Algebras

23 pages, AMS-LaTeX2e

Scientific paper

In the context of A. Connes' spectral triples, a suitable notion of morphism is introduced. Discrete groups with length function provide a natural example for our definitions. A. 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.

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