two constructions of spectral triples

Olivier Gabriel (University of Glasgow)

Tuesday 25th November, 2014 16:00-17:00 Maths 416


The aim of this talk is to generalise the constructions of spectral triples
on noncommutative tori and Quantum Heisenberg Manifolds (QHM) to broader
settings. After a few reminders about noncommutative tori and spectral
triples, we prove that an ergodic action of a compact Lie group G on a
unital C*-algebra A yields a natural spectral triple structure on A. In the
second part, we investigate "permanence properties" for the previous sort
of spectral triples. We first introduce the notion of Generalised Crossed
Product (GCP) and illustrate it by the case of QHM. A GCP contains a
sub-C*-algebra called its "basis". A spectral triple on the basis can
induce a spectral triple on the GCP, under some assumptions which we make

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