Built on

L. Dabrowski, Group Actions on Spinors. Lecture Notes. Bibliopolis, Naples, ( 1988 ) (1988) (without proofs correction)
1988
Earlier work this paper cites.
M. Dubois-Violette, R. Kerner, J. Madore, Gauge bosons in a non-commutative geometry, Phys. Lett. B 217 217 485 − 488 , 485-488, ( 1989 ) . (1989)
1989
Earlier work this paper cites.
A. Connes, J. Lott, Particles models and noncommutative geometry, Nucl. Phys B 18 B18 Suppl., 29 − 47 , 29-47, ( 1990 ) . (1990)
1990
Earlier work this paper cites.
M. Dubois-Violette, Noncommutative differential geometry, quantum mechanics and gauge theory, In: Bartocci C., Bruzzo U., Cianci R. (eds) Differential Geometric Methods in Theoretical Physics, Lect. Notes Phys. 375 375 , Springer, ( 1991 ) . (1991)
1991
Earlier work this paper cites.
A. Connes Noncommutative geometry, Academic Press, ( 1994 ) . (1994)
1994
Earlier work this paper cites.
A. Chamseddine, A. Connes, The spectral action principle, Commun. Math. Phys. 186 , 186, 731 − 750 , 731-750, ( 1997 ) . (1997). arXiv:hep-th/9606001v1
1997
Earlier work this paper cites.
J. Gracia-Bondía M, J.C. Varilly, G. Figueroa, Elements of noncommutative geometry, Birkhauser Advanced Texts, Basler Lehrbucher, ( 2001 ) . (2001)
2001
Earlier work this paper cites.
A. Connes, G. Landi, Noncommutative Manifolds the Instanton Algebra and Isospectral Deformations, Commun.,Math.,Phys. 221 , 221, pp. 141 − 159 , 141-159, ( 2001 ) . (2001). arXiv:math/0011194v3
2001
Earlier work this paper cites.
A. Connes, M. Dubois-Violette ”Noncommutative finite-dimensional manifolds. I. Spherical manifolds and related examples”
2002
Earlier work this paper cites.

Similar

M. Paschke, A. Sitarz, On Spin Structures and Dirac Operators on the Noncommutative Torus, Lett. Math. Phys.77, 317-327, ( 2006 ) . (2006). arXiv:math/0605191v1
2006
Cited alongside, same era.
A. Connes, M. Marcolli, Noncommutative geometry, quantum fields and motives, American Mathematical Society, ( 2008 ) . (2008)
2008
Cited alongside, same era.
L. Dąbrowski, Spinors and theta deformation, Russ. J. Math. Phys. 16 16 , 404 − 408 , 404-408, ( 2009 ) . (2009). arXiv:0808.0440v1
Original
2009
Cited alongside, same era.
A. Connes, P. Tretkoff, The Gauss-Bonnet theorem for the noncommutative torus, ( 2009 ) . (2009). arXiv:0910.0188v1
Original
2009
Cited alongside, same era.
F. Fathizadeh, M. Khalkhali, The Gauss-Bonnet theorem for noncommutative two tori with a general conformal structure J. Noncommut. Geom. 6 , 6, ( 2010 ) . (2010). arXiv:1110.3511v1

Then

L. Dąbrowski, A. Sitarz, Curved noncommutative torus and Gauss-Bonnet, J. Math. Phys. 54 54 , 013518 (2013). arXiv: 1204.0420 v 1 , 1204.0420v1,
2013
Later among the works it cites.
W. van Suijlekom, Noncommutative Geometry and Particle Physics, Springer, ( 2014 ) . (2014)
2014
Later among the works it cites.
A. Devastato, F. Lizzi, P. Martinetti, Grand Symmetry, Spectral Action, and the Higgs mass, JGEP 42 , 42, ( 2014 ) . (2014). arXiv:1403.7567v2
Original
2014
Later among the works it cites.
J. Boeijink, K. van den Dungen, On globally non-trivial almost-commutative manifolds, J. Math. Phys. 55 55 , 103508 , 103508, ( 2014 ) . (2014). arXiv:1405.5368v2
Original
2014
Later among the works it cites.
L. Dąbrowski, A. Sitarz, An asymmetric nonccomutative torus, SIGMA 11 , 11, ( 2015 ) . (2015). arXiv:1406.4645v3
Original

Beyond the bibliography

alphaXiv searches the wider corpus for related work and actual follow-ups.

Open on alphaXiv

alphaXiv is searching for related work…

Reading the bibliography…

2018

Spin geometry of the rational noncommutative torus

Carotenuto, Alessandro, Dabrowski, Ludwik

Understand

The twined almost commutative structure of the standard spectral triple on the noncommutative torus with rational parameter is exhibited, by showing isomorphisms with a spectral triple on the algebra of sections of certain bundle of algebras, and a spectral triple on a certain invariant subalgebra of the product algebra.

These isomorphisms intertwine also the grading and real structure.
This holds for all four inequivalent spin structures, which are explicitly constructed in terms of double coverings of the noncommutative torus (with arbitrary real parameter).
These results are extended also to a class of curved (non flat) spectral triples, obtained as a perturbation of the standard one by eight central elements.

Built on

L. Dabrowski, Group Actions on Spinors. Lecture Notes. Bibliopolis, Naples, ( 1988 ) (1988) (without proofs correction)
1988
Earlier work this paper cites.
M. Dubois-Violette, R. Kerner, J. Madore, Gauge bosons in a non-commutative geometry, Phys. Lett. B 217 217 485 − 488 , 485-488, ( 1989 ) . (1989)
1989
Earlier work this paper cites.
A. Connes, J. Lott, Particles models and noncommutative geometry, Nucl. Phys B 18 B18 Suppl., 29 − 47 , 29-47, ( 1990 ) . (1990)
1990
Earlier work this paper cites.
M. Dubois-Violette, Noncommutative differential geometry, quantum mechanics and gauge theory, In: Bartocci C., Bruzzo U., Cianci R. (eds) Differential Geometric Methods in Theoretical Physics, Lect. Notes Phys. 375 375 , Springer, ( 1991 ) . (1991)
1991
Earlier work this paper cites.
A. Connes Noncommutative geometry, Academic Press, ( 1994 ) . (1994)
1994
Earlier work this paper cites.
A. Chamseddine, A. Connes, The spectral action principle, Commun. Math. Phys. 186 , 186, 731 − 750 , 731-750, ( 1997 ) . (1997). arXiv:hep-th/9606001v1
1997
Earlier work this paper cites.
J. Gracia-Bondía M, J.C. Varilly, G. Figueroa, Elements of noncommutative geometry, Birkhauser Advanced Texts, Basler Lehrbucher, ( 2001 ) . (2001)
2001
Earlier work this paper cites.
A. Connes, G. Landi, Noncommutative Manifolds the Instanton Algebra and Isospectral Deformations, Commun.,Math.,Phys. 221 , 221, pp. 141 − 159 , 141-159, ( 2001 ) . (2001). arXiv:math/0011194v3
2001
Earlier work this paper cites.
A. Connes, M. Dubois-Violette ”Noncommutative finite-dimensional manifolds. I. Spherical manifolds and related examples”
2002
Earlier work this paper cites.