2012/04/19 by Alan L. T. Paterson, Paterson, Alan L. T.
Mathematics · #46L55 #58B34 #Advanced Algebra and Geometry #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Operator Algebras (math.OA) #math.OA #msc:46L55 #msc:58B34
paper · pdf · doi:10.48550/arxiv.1204.4404
20 pages
arxiv created 2012/04/19 · openalex publication_date 2012/04/19 · arxiv updated 2012/04/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Connes showed that spectral triples encode (noncommutative) metric information. Further, Connes and Moscovici in their metric bundle construction showed that, as with the Takesaki duality theorem, forming a crossed product spectral triple can substantially simplify the structure. In a recent paper, Bellissard, Marcolli and Reihani (among other things) studied in depth metric notions for spectral triples and crossed product spectral triples for Z-actions, with applications in number theory and coding theory. In the work of Connes and Moscovici, crossed products involving groups of diffeomorphisms and even of étale groupoids are required. With this motivation, the present paper develops part of the Bellissard-Marcolli-Reihani theory for a general discrete group action, and in particular, introduces coaction spectral triples and their associated metric notions. The isometric condition is replaced by the contractive condition.