Spectral triples from bimodule connections and Chern connections

2015/08/19 by Edwin Beggs, Shahn Majid, Beggs, Edwin +1
Mathematics · Physics and Astronomy · #58B32 #81R50 #83C57 #FOS: Mathematics #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #High Energy Physics - Theory (hep-th) #Quantum Algebra (math.QA) #gr-qc #hep-th #math.QA #msc:58B32 #msc:81R50 #msc:83C57

paper · pdf · doi:10.48550/arxiv.1508.04808

26 pages Latex - replaced to add a reference and fix some typos

arxiv created 2015/09/03 · arxiv updated 2015/09/04

Abstract

We give a geometrical construction of Connes spectral triples or noncommutative Dirac operators D starting with a bimodule connection on the proposed spinor bundle. The theory is applied to the example of M₂(\Bbb C), and also applies to the standard q-sphere and the q-disk with the right classical limit and all properties holding except for \mathcal J now being a twisted isometry. We also describe a noncommutative Chern construction from holomorphic bundles which in the q-sphere case provides the relevant bimodule connection.

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