@inbook {Arici2016,
	title = {Pimsner Algebras and Circle Bundles},
	booktitle = {Noncommutative Analysis, Operator Theory and Applications},
	year = {2016},
	pages = {1{\textendash}25},
	publisher = {Springer International Publishing},
	organization = {Springer International Publishing},
	address = {Cham},
	abstract = {<p>We report on the connections between noncommutative principal circle bundles, Pimsner algebras and strongly graded algebras. We illustrate several results with examples of quantum weighted projective and lens spaces and θ-deformations.</p>},
	isbn = {978-3-319-29116-1},
	doi = {10.1007/978-3-319-29116-1_1},
	url = {https://doi.org/10.1007/978-3-319-29116-1_1},
	author = {Francesca Arici and Francesco D{\textquoteright}Andrea and Giovanni Landi},
	editor = {Alpay, Daniel and Cipriani, Fabio and Colombo, Fabrizio and Guido, Daniele and Sabadini, Irene and Sauvageot, Jean-Luc}
}
@article {2014,
	title = {Quantum gauge symmetries in noncommutative geometry},
	number = {Journal of Noncommutative Geometry;volume 8; issue 2; pages 433-471;},
	year = {2014},
	publisher = {European Mathematical Society Publishing House},
	abstract = {We discuss generalizations of the notion of i) the group of unitary elements of a (real or complex) finite-dimensional C*-algebra, ii) gauge transformations and iii) (real) automorphisms in the framework of compact quantum group theory and spectral triples. The quantum analogue of these groups are defined as universal (initial) objects in some natural categories. After proving the existence of the universal objects, we discuss several examples that are of interest to physics, as they appear in the noncommutative geometry approach to particle physics: in particular, the C*-algebras M n(R), Mn(C) and Mn(H), describing the finite noncommutative space of the Einstein-Yang-Mills systems, and the algebras A F = C H M3 (C) and Aev = H H M4(C), that appear in Chamseddine-Connes derivation of the Standard Model of particle physics coupled to gravity. As a byproduct, we identify a "free" version of the symplectic group Sp.n/ (quaternionic unitary group).},
	doi = {10.4171/JNCG/161},
	url = {http://urania.sissa.it/xmlui/handle/1963/34897},
	author = {Jyotishman Bhowmick and Francesco D{\textquoteright}Andrea and Biswarup Krishna Das and Ludwik Dabrowski}
}
@article {2011,
	title = {Quantum Isometries of the finite noncommutative geometry of the Standard  Model},
	journal = {Commun. Math. Phys. 307:101-131, 2011},
	number = {arXiv:1009.2850;},
	year = {2011},
	publisher = {Springer},
	abstract = {We compute the quantum isometry group of the finite noncommutative geometry F describing the internal degrees of freedom in the Standard Model of particle physics. We show that this provides genuine quantum symmetries of the spectral triple corresponding to M x F where M is a compact spin manifold. We also prove that the bosonic and fermionic part of the spectral action are preserved by these symmetries.},
	doi = {10.1007/s00220-011-1301-2},
	url = {http://hdl.handle.net/1963/4906},
	author = {Jyotishman Bhowmick and Francesco D{\textquoteright}Andrea and Ludwik Dabrowski}
}
@article {2010,
	title = {Dirac Operators on Quantum Projective Spaces},
	journal = {Comm. Math. Phys. 295 (2010) 731-790},
	number = {SISSA;17/2009/FM},
	year = {2010},
	note = {Quantum Algebra},
	abstract = {We construct a family of self-adjoint operators D_N which have compact resolvent and bounded commutators with the coordinate algebra of the quantum projective space CP_q(l), for any l>1 and 0<q<1. They provide 0^+ dimensional equivariant even spectral triples. If l is odd and N=(l+1)/2, the spectral triple is real with KO-dimension 2l mod 8.},
	doi = {10.1007/s00220-010-0989-8},
	url = {http://hdl.handle.net/1963/3606},
	author = {Francesco D{\textquoteright}Andrea and Ludwik Dabrowski}
}
@article {2008,
	title = {The Isospectral Dirac Operator on the 4-dimensional Orthogonal Quantum Sphere},
	journal = {Comm. Math. Phys. 279 (2008) 77-116},
	number = {SISSA;95/2007/MP},
	year = {2008},
	abstract = {Equivariance under the action of Uq(so(5)) is used to compute the left regular and (chiral) spinorial representations of the algebra of the quantum Euclidean 4-sphere S^4_q. These representations are the constituents of a spectral triple on this sphere with a Dirac operator which is isospectral to the canonical one of the spin structure of the round undeformed four-sphere and which gives metric dimension four for the noncommutative geometry. Non-triviality of the geometry is proved by pairing the associated Fredholm module with an {\textquoteleft}instanton\\\' projection. A real structure which satisfies all required properties modulo a suitable ideal of {\textquoteleft}infinitesimals\\\' is also introduced.},
	doi = {10.1007/s00220-008-0420-x},
	url = {http://hdl.handle.net/1963/2567},
	author = {Francesco D{\textquoteright}Andrea and Ludwik Dabrowski and Giovanni Landi}
}
@article {2008,
	title = {The Noncommutative Geometry of the Quantum Projective Plane},
	journal = {Rev. Math. Phys. 20 (2008) 979-1006},
	number = {SISSA;100/2007/MP},
	year = {2008},
	abstract = {We study the spectral geometry of the quantum projective plane CP^2_q. In particular, we construct a Dirac operator which gives a 0^+ summable triple, equivariant under U_q(su(3)).},
	doi = {10.1142/S0129055X08003493},
	url = {http://hdl.handle.net/1963/2548},
	author = {Francesco D{\textquoteright}Andrea and Ludwik Dabrowski and Giovanni Landi}
}
@article {2007,
	title = {Dirac operators on all Podles quantum spheres},
	journal = {J. Noncomm. Geom. 1 (2007) 213-239},
	number = {arXiv.org;math/0606480v2},
	year = {2007},
	abstract = {We construct spectral triples on all Podles quantum spheres. These noncommutative geometries are equivariant for a left action of $U_q(su(2))$ and are regular, even and of metric dimension 2. They are all isospectral to the undeformed round geometry of the 2-sphere. There is also an equivariant real structure for which both the commutant property and the first order condition for the Dirac operators are valid up to infinitesimals of arbitrary order.},
	doi = {10.4171/JNCG/5},
	url = {http://hdl.handle.net/1963/2177},
	author = {Francesco D{\textquoteright}Andrea and Ludwik Dabrowski and Giovanni Landi and Elmar Wagner}
}
@mastersthesis {2007,
	title = {Noncommutative geometry and quantum group symmetries},
	year = {2007},
	school = {SISSA},
	abstract = {It is a widespread belief that mathematics originates from the desire to understand (and eventually to formalize) some aspects of the real world. Quoting [Man07],   {\guillemotleft}we are doing mathematics in order to understand, create, and handle things, and perhaps this understanding is mathematics{\guillemotright}  . Let me thus begin with a brief discussion of the physical ideas that motivated the development of Noncommutative Geometry and Quantum Group Theory - the areas of mathematics to which this dissertation belongs. Some physicists believe, and Einstein himself expressed this view in [Ein98a], that physics progresses in stages: there is no {\textquoteleft}final\\\' theory of Nature, but simply a sequence of theories which provide more and more accurate descriptions of the real world...},
	keywords = {Noncommutative geometry},
	url = {http://hdl.handle.net/1963/5269},
	author = {Francesco D{\textquoteright}Andrea}
}
@article {2006,
	title = {A cyclic integral on k-Minkowski noncommutative space-time},
	journal = {Int. J. Mod. Phys. A 21 (2006) 3133-3150},
	number = {arXiv.org;hep-th/0407227v1},
	year = {2006},
	abstract = {We examine some alternative possibilities for an action functional for $\\\\kappa$-Minkowski noncommutative spacetime, with an approach which should be applicable to other spacetimes with coordinate-dependent commutators of the spacetime coordinates ($[x_\\\\mu,x_\\\\nu]=f_{\\\\mu,\\\\nu}(x)$). Early works on $\\\\kappa$-Minkowski focused on $\\\\kappa$-Poincar\\\\\\\'e covariance and the dependence of the action functional on the choice of Weyl map, renouncing to invariance under cyclic permutations of the factors composing the argument of the action functional. A recent paper (hep-th/0307149), by Dimitrijevic, Jonke, Moller, Tsouchnika, Wess and Wohlgenannt, focused on a specific choice of Weyl map and, setting aside the issue of $\\\\kappa$-Poincar\\\\\\\'e covariance of the action functional, introduced in implicit form a cyclicity-inducing measure. We provide an explicit formula for (and derivation of) a choice of measure which indeed ensures cyclicity of the action functional, and we show that the same choice of measure is applicable to all the most used choices of Weyl map. We find that this {\textquoteleft}{\textquoteleft}cyclicity-inducing measure\\\'\\\' is not covariant under $\\\\kappa$-Poincar\\\\\\\'e transformations. We also notice that the cyclicity-inducing measure can be straightforwardly derived using a map which connects the $\\\\kappa$-Minkowski spacetime coordinates and the spacetime coordinates of a {\textquoteleft}{\textquoteleft}canonical\\\'\\\' noncommutative spacetime, with coordinate-independent commutators.},
	doi = {10.1142/S0217751X06031077},
	url = {http://hdl.handle.net/1963/2158},
	author = {Alessandra Agostini and Giovanni Amelino-Camelia and Michele Arzano and Francesco D{\textquoteright}Andrea}
}
@article {2006,
	title = {Local Index Formula on the Equatorial Podles Sphere},
	number = {SISSA;85/2005/FM},
	year = {2006},
	abstract = {We discuss spectral properties of the equatorial Podles sphere. As a preparation we also study the {\textquoteleft}degenerate\\\' (i.e. $q=0$) case (related to the quantum disk). We consider two different spectral triples: one related to the Fock representation of the Toeplitz algebra and the isopectral one....},
	doi = {10.1007/s11005-005-0047-1},
	url = {http://hdl.handle.net/1963/1782},
	author = {Francesco D{\textquoteright}Andrea and Ludwik Dabrowski}
}
@article {2006,
	title = {Spectral geometry of k-Minkowski space},
	journal = {J. Math. Phys. 47 (2006) 062105},
	number = {arXiv.org;hep-th/0503012v4},
	year = {2006},
	abstract = {<p>After recalling Snyder{\textquoteright}s idea of using vector fields over a smooth manifold as "coordinates on a noncommutative space", we discuss a two dimensional toy-model whose "dual" noncommutative coordinates form a Lie algebra: this is the well known $\kappa$-Minkowski space. We show how to improve Snyder{\textquoteright}s idea using the tools of quantum groups and noncommutative geometry. We find a natural representation of the coordinate algebra of $\kappa$-Minkowski as linear operators on an Hilbert space study its "spectral properties" and discuss how to obtain a Dirac operator for this space. We describe two Dirac operators. The first is associated with a spectral triple. We prove that the cyclic integral of M. Dimitrijevic et al. can be obtained as Dixmier trace associated to this triple. The second Dirac operator is equivariant for the action of the quantum Euclidean group, but it has unbounded commutators with the algebra.</p>},
	doi = {10.1063/1.2204808},
	url = {http://hdl.handle.net/1963/2131},
	author = {Francesco D{\textquoteright}Andrea}
}
