scholarly journals On the Chern-Gauss-Bonnet Theorem and Conformally Twisted Spectral Triples for C*-Dynamical Systems

2016 ◽  
Author(s):  
Farzad Fathizadeh ◽  
◽  
Olivier Gabriel ◽  
Keyword(s):  
Dynamical Systems ◽  
Spectral Triples ◽  
Bonnet Theorem ◽  
Twisted Spectral Triples

scholarly journals Gauge transformations for twisted spectral triples

2018 ◽  
Vol 108 (12) ◽  
pp. 2589-2626 ◽  
Author(s):  
Giovanni Landi ◽  
Pierre Martinetti
Keyword(s):  
Spectral Triples ◽  
Gauge Transformations ◽  
Twisted Spectral Triples

scholarly journals On the Gauss-Bonnet for the quasi-Dirac operators on the sphere

2017 ◽  
Vol 50 (1) ◽  
pp. 66-71
Author(s):  
Andrzej Sitarz
Keyword(s):  
Scalar Curvature ◽  
Dirac Operators ◽  
Two Dimensional ◽  
Spectral Triples ◽  
Bonnet Theorem

Abstract We investigate examples of Gauss-Bonnet theorem and the scalar curvature for the two-dimensional commutative sphere with quasi-spectral triples obtained by modifying the order-one condition.

scholarly journals Spectral triples on irreversible C∗-dynamical systems

2021 ◽  
Author(s):  
Valeriano Aiello ◽  
Daniele Guido ◽  
Tommaso Isola
Keyword(s):  
Dynamical Systems ◽  
Product Formula ◽  
Crossed Product ◽  
Spectral Triple ◽  
Crossed Products ◽  
Spectral Triples ◽  
Main Assumption ◽  
Noncommutative Spaces ◽  
Covering Projection ◽  
Injective Endomorphism

Given a spectral triple on a [Formula: see text]-algebra [Formula: see text] together with a unital injective endomorphism [Formula: see text], the problem of defining a suitable crossed product [Formula: see text]-algebra endowed with a spectral triple is addressed. The proposed construction is mainly based on the works of Cuntz and [A. Hawkins, A. Skalski, S. White and J. Zacharias, On spectral triples on crossed products arising from equicontinuous actions, Math. Scand. 113(2) (2013) 262–291], and on our previous papers [V. Aiello, D. Guido and T. Isola, Spectral triples for noncommutative solenoidal spaces from self-coverings, J. Math. Anal. Appl. 448(2) (2017) 1378–1412; V. Aiello, D. Guido and T. Isola, A spectral triple for a solenoid based on the Sierpinski gasket, SIGMA Symmetry Integrability Geom. Methods Appl. 17(20) (2021) 21]. The embedding of [Formula: see text] in [Formula: see text] can be considered as the dual form of a covering projection between noncommutative spaces. A main assumption is the expansiveness of the endomorphism, which takes the form of the local isometricity of the covering projection, and is expressed via the compatibility of the Lip-norms on [Formula: see text] and [Formula: see text].

Twisted spectral triples and covariant differential calculi

2011 ◽  
Vol 93 ◽  
pp. 177-188 ◽  
Author(s):  
Ulrich Krähmer ◽  
Elmar Wagner
Keyword(s):  
Spectral Triples ◽  
Twisted Spectral Triples

scholarly journals Lorentz signature and twisted spectral triples

2018 ◽  
Vol 2018 (3) ◽  
Author(s):  
A. Devastato ◽  
S. Farnsworth ◽  
F. Lizzi ◽  
P. Martinetti
Keyword(s):  
Spectral Triples ◽  
Twisted Spectral Triples

scholarly journals Regularity of twisted spectral triples and pseudodifferential calculi

2019 ◽  
Vol 13 (3) ◽  
pp. 985-1009
Author(s):  
Marco Matassa ◽  
Robert Yuncken
Keyword(s):  
Spectral Triples ◽  
Twisted Spectral Triples

scholarly journals Real Part of Twisted-by-Grading Spectral Triples

2020 ◽  
Author(s):  
Manuele Filaci ◽  
◽  
Pierre Martinetti ◽  
◽  
◽  
...  
Keyword(s):  
Standard Model ◽  
Spectral Triple ◽  
Spectral Triples ◽  
The Real ◽  
Initial Algebra ◽  
The Standard Model ◽  
Twisted Spectral Triples

After a brief review on the applications of twisted spectral triples to physics, we adapt to the twisted case the notion of real part of a spectral triple. In particular, when one twists a usual spectral triple by its grading, we show that - depending on the KO dimension - the real part is either twisted as well, or is the intersection of the initial algebra with its opposite. We illustrate this result with the spectral triple of the standard model.

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