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The leitmotiv of this review is noncommutative principal U(1)-bundles and associated line bundles.
A. Bahri, M. Franz, D. Notbohm and N. Ray, The classification of weighted projective spaces
1938
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P. Guillot and C. Kassel, Cohomology of Invariant Drinfeld Twists on Group Algebras
1939
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F. Arici, Principal circle bundles, Pimsner algebras and Gysin sequences
1963
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A.L. Onishchik, Some concepts and applications of the theory of non-abelian cohomology
1967
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M. Sweedler, Hopf Algebras
1969
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J. Giraud, Cohomologie non-abélienne
1971
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E.J. Taft, The order of the antipode of finite-dimensional Hopf algebra
1971
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M.A. Rieffel, Morita Equivalence for C ∗ C^{*} -and W ∗ W^{*} -algebras
1974
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A. Connes, C ∗ C^{*} -algèbres et géométrie différentielle
1980
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W.P. Thurston, The Geometry and Topology of Three-Manifolds
1980
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B. Pareigis, A noncommutative noncocommutative Hopf algebra in “nature”
1981
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K.H. Ulbrich, Vollgraduierte Algebren
1981
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C. Nastasescu and F. Van Oystaeyen, Graded ring theory
1982
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M.A. Rieffel, Morita equivalence for operator algebras
1982
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M.A. Rieffel, The cancellation theorem for projective modules over irrational rotation C ∗ C^{*} -algebras
1983
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S.L. Woronowicz, Compact matrix pseudogroups
1987
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G.B. Folland, Harmonic analysis in phase space
1989
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V.G. Drinfeld, Quasi-Hopf algebras
1990
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V.G. Drinfeld, On quasitriangular quasi-Hopf algebras and a group closely connected with Gal ( ℚ ¯ / ℚ ) \mathrm{Gal}(\bar{\mathbb{Q}}/\mathbb{Q})
1991
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L. Vaksman and Ya. Soibelman, The algebra of functions on the quantum group S U ( n + 1 ) SU(n+1) and odd-dimensional quantum spheres
1991
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S. Montgomery, Hopf algebras and their actions on rings
1993
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V. Chari and A.N. Pressley, A guide to quantum groups
1994
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H.J. Schneider, Hopf Galois Extensions, Crossed Products, and Clifford Theory
1994
Cited alongside, same era.
T. Brzezinski and S. Majid, Quantum group gauge theory on quantum spaces
1995
Cited alongside, same era.
S. Majid, Foundations of quantum group theory
1995
Cited alongside, same era.
U. Meyer, Projective quantum spaces
1995
Cited alongside, same era.
P. Podles, Symmetries of quantum spaces. Subgroups and quotient spaces of quantum S U ( 2 ) SU(2) and S O ( 3 ) SO(3) groups
1995
Cited alongside, same era.
M. Đurđević, Geometry of quantum principal bundles I
1996
Cited alongside, same era.
Y.I. Manin, Real multiplication and noncommutative geometry
2004
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J. Bichon and G. Carnovale, Lazy cohomology: an analogue of the Schur multiplier for arbitrary Hopf algebras
2005
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H. Albuquerque and S. Majid, New approach to Octonions and Cayley algebras
2006
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J.C. Várilly, An introduction to noncommutative geometry
2006
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D.P. Williams, Crossed Products of C ∗ C^{*} -Algebras
2007
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J. Plazas, Arithmetic structures on noncommutative tori with real multiplication
2008
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P.M. Hajac, Strong connections on quantum principal bundles , Comm. Math. Phys. 182 (1996), 579–617; doi: 10.1007/BF02506418 , arXiv: hep-th/9406129
1996
Cited alongside, same era.
M. Đurđević, Geometry of quantum principal bundles II
1997
Cited alongside, same era.
A. Klimyk and K. Schmüdgen, Quantum groups and their representations
1997
Cited alongside, same era.
M.V. Pimsner, A class of C ∗ C^{*} -algebras
1997
Cited alongside, same era.
H. Albuquerque and S. Majid, Quasialgebra Structure of the Octonions
1998
Cited alongside, same era.
N.P. Landsman, Topics Between Classical And Quantum Mechanics
1998
Cited alongside, same era.
2009
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S. Montgomery, Hopf Galois theory: A survey
2009
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E.J. Beggs and S. Majid, Quantization by cochain twists and nonassociative differentials
2010
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E.J. Beggs and S. Majid, Nonassociative Riemannian geometry by twisting
2010
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F. D’Andrea and L. Dabrowski, Dirac operators on Quantum Projective Spaces
2010
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F. D’Andrea and G. Landi, Bounded and unbounded Fredholm modules for quantum projective spaces
2010
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2011
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P.M. Hajac, U. Kraehmer, R. Matthes and B. Zielinski, Piecewise principal comodule algebras
2011
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2014
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F. D’Andrea, G. Fiore and D. Franco, Modules over the noncommutative torus and elliptic curves
2014
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2014
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2015
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C. Esposito, Formality Theory: From Poisson Structures to Deformation Quantization
2015
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