Dirac operator associated to a quantum metric
Shahn Majid
Queen Mary University of London, UK
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Abstract
We construct a canonical geometrically realised Connes spectral triple or ‘Dirac operator’ from the data of a quantum metric and a bimodule connection on , at the pre-Hilbert space level. Here is a possibly noncommutative coordinate algebra, a bimodule of -forms and the spinor bundle is . When applied to graphs or lattices, we essentially recover a previously proposed Dirac operator but now as a geometrically realised spectral triple. We also apply the construction to the fuzzy sphere and to matrices with their standard quantum Riemannian geometries. We propose how can be extended to an external bundle with bimodule connection.
Cite this article
Shahn Majid, Dirac operator associated to a quantum metric. J. Noncommut. Geom. (2024), published online first
DOI 10.4171/JNCG/570