Contractive Spectral Triples for Crossed Products

  • Alan L. T. Paterson

Abstract

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 ├ętale 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.
Published
2014-05-06
How to Cite
Paterson, A. L. T. (2014). Contractive Spectral Triples for Crossed Products. MATHEMATICA SCANDINAVICA, 114(2), 275-298. https://doi.org/10.7146/math.scand.a-17112
Section
Articles