,
pages 183-201
Spectral Triples on O N
Publication type: Book Chapter
Publication date: 2018-04-10
Abstract
We give a construction of an odd spectral triple on the Cuntz algebra O
N
, whose K-homology class generates the odd K-homology group K
1(O
N
). Using a metric measure space structure on the Cuntz-Renault groupoid, we introduce a singular integral operator which is the formal analogue of the logarithm of the Laplacian on a Riemannian manifold. Assembling this operator with the infinitesimal generator of the gauge action on O
N
yields a θ-summable spectral triple whose phase is finitely summable. The relation to previous constructions of Fredholm modules and spectral triples on O
N
is discussed.
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TY - GENERIC
DO - 10.1007/978-3-319-72299-3_9
UR - https://doi.org/10.1007/978-3-319-72299-3_9
TI - Spectral Triples on O N
T2 - MATRIX Book Series
AU - Goffeng, Magnus
AU - Mesland, Bram
PY - 2018
DA - 2018/04/10
PB - Springer Nature
SP - 183-201
SN - 2523-3041
SN - 2523-305X
ER -
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@incollection{2018_Goffeng,
author = {Magnus Goffeng and Bram Mesland},
title = {Spectral Triples on O N},
publisher = {Springer Nature},
year = {2018},
pages = {183--201},
month = {apr}
}