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Differential Calculus on Quantum Spheres  [PDF]
Martin Welk
Mathematics , 1998,
Abstract: We study covariant differential calculus on the quantum spheres S_q^2N-1. Two classification results for covariant first order differential calculi are proved. As an important step towards a description of the noncommutative geometry of the quantum spheres, a framework of covariant differential calculus is established, including a particular first order calculus obtained by factorization, higher order calculi and a symmetry concept.
Quantum isometries and noncommutative spheres  [PDF]
Teodor Banica,Debashish Goswami
Mathematics , 2009, DOI: 10.1007/s00220-010-1060-5
Abstract: We introduce and study two new examples of noncommutative spheres: the half-liberated sphere, and the free sphere. Together with the usual sphere, these two spheres have the property that the corresponding quantum isometry group is "easy", in the representation theory sense. We present as well some general comments on the axiomatization problem, and on the "untwisted" and "non-easy" case.
Jordanian quantum spheres  [PDF]
R. Chakrabarti,J. Segar
Mathematics , 2001, DOI: 10.1142/S0217732301004832
Abstract: We introduce and investigate a one parameter family of quantum spaces invariant under the left (right) coactions of the group-like element ${\cal T}_{h}^{(j=1)}$ of the Jordanian function algebra $Fun_{h}(SL(2))$. These spaces may be regarded as Jordanian quantization of the two-dimensional spheres.
Thermodynamics of quantum photon spheres  [PDF]
M. C. Baldiotti,Walace S. Elias,C. Molina,Thiago S. Pereira
Physics , 2014, DOI: 10.1103/PhysRevD.90.104025
Abstract: Photon spheres, surfaces where massless particles are confined in closed orbits, are expected to be common astrophysical structures surrounding ultracompact objects. In this paper a semiclassical treatment of a photon sphere is proposed. We consider the quantum Maxwell field and derive its energy spectra. A thermodynamic approach for the quantum photon sphere is developed and explored. Within this treatment, an expression for the spectral energy density of the emitted radiation is presented. Our results suggest that photon spheres, when thermalized with their environment, have nonusual thermodynamic properties, which could lead to distinct observational signatures.
Quantum symmetry groups of noncommutative spheres  [PDF]
Joseph C. Varilly
Mathematics , 2001, DOI: 10.1007/s002200100490
Abstract: We show that the noncommutative spheres of Connes and Landi are quantum homogeneous spaces for certain compact quantum groups. We give a general construction of homogeneous spaces which support noncommutative spin geometries.
Geometry of Quantum Spheres  [PDF]
Ludwik Dabrowski
Mathematics , 2005, DOI: 10.1016/j.geomphys.2005.04.003
Abstract: Spectral triples on the q-deformed spheres of dimension two and three are reviewed.
Dirac operators on quantum two spheres  [PDF]
K. Ohta,H. Suzuki
Physics , 1994, DOI: 10.1142/S0217732394002197
Abstract: We investigate the spin $1/2$ fermions on quantum two spheres. It is shown that the wave functions of fermions and a Dirac Operator on quantum two spheres can be constructed in a manifestly covariant way under the quantum group $SU(2)_q$. The concept of total angular momentum and chirality can be expressed by using $q$-analog of Pauli-matrices and appropriate commutation relations.
Noncommutative Balls and Mirror Quantum Spheres  [PDF]
Jeong Hee Hong,Wojciech Szymanski
Mathematics , 2007, DOI: 10.1112/jlms/jdn003
Abstract: Noncommutative analogues of n-dimensional balls are defined by repeated application of the quantum double suspension to the classical low-dimensional spaces. In the `even-dimensional' case they correspond to the Twisted Canonical Commutation Relations of Pusz and Woronowicz. Then quantum spheres are constructed as double manifolds of noncommutative balls. Both C*-algebras and polynomial algebras of the objects in question are defined and analyzed, and their relations with previously known examples are presented. Our construction generalizes that of Hajac, Matthes and Szymanski for `dimension 2', and leads to a new class of quantum spheres (already on the C*-algebra level) in all `even-dimensions'.
Non-commutative Chern Characters of the C*-Algebras of spheres and quantum spheres  [PDF]
Nguyen Quoc Tho
Mathematics , 1999,
Abstract: We propose in this paper the construction of non-commutative Chern characters of the C*-algebras of spheres and quantum spheres. The final computation gives us a clear relation with the ordinary Z/(2)-graded Chern characters of tori or their normalizers.
Twisted Dirac Operators over Quantum Spheres  [PDF]
Andrzej Sitarz
Mathematics , 2007, DOI: 10.1063/1.2842067
Abstract: We construct new families of spectral triples over quantum spheres, with a particular attention focused on the standard Podles quantum sphere and twisted Dirac operators.
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