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Twisted Reality Condition for Dirac Operators
Motivated by examples obtained from conformal deformations of spectral triples and a spectral triple construction on quantum cones, we propose a new...
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The Geometry of Quantum Lens Spaces: Real Spectral Triples and Bundle Structure
We study almost real spectral triples on quantum lens spaces, as orbit spaces of free actions of cyclic groups on the spectral geometry on the...
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Non-Commutative Integration, Zeta Functions and the Haar State for SU q (2)
We study a notion of non-commutative integration, in the spirit of modular spectral triples, for the quantum group SU q (2). In particular we define...
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Weighted Circle Actions on the Heegaard Quantum Sphere
Weighted circle actions on the quantum Heeqaard 3-sphere are considered. The fixed point algebras, termed quantum weighted Heegaard spheres, and...
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Operator Algebra Quantum Homogeneous Spaces of Universal Gauge Groups
In this paper, we quantize universal gauge groups such as SU (∞), as well as their homogeneous spaces, in the σ - C *-algebra setting. More precisely, we...
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Coherent States for Hopf Algebras
Families of Perelomov coherent states are defined axiomatically in the context of unitary representations of Hopf algebras. A global geometric...
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Algebraic Approach to Quantum Gravity III: Non-Commmutative Riemannian Geometry
This is a self-contained introduction to quantum Riemannian geometry based on quantum groups as frame groups, and its proposed role in quantum...
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Para-Hopf Algebroids and their Cyclic Cohomology
We introduce the concept of para-Hopf algebroid and define their cyclic cohomology in the spirit of Connes–Moscovici cyclic cohomology for Hopf...
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Dirac Operators on Quantum Flag Manifolds
A Dirac operator D on quantized irreducible generalized flag manifolds is defined. This yields a Hilbert space realization of the covariant...
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Differential Calculus on Quantum Homogeneous Spaces
The notion of quantum tangent space of a covariant first-order differential calculus over a quantum homogeneous space is established.
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Noncommutative Ricci Curvature and Dirac Operator on C q [SL2] at Roots of Unity
We find a unique torsion free Riemannian spin connection for the natural Killing metric on the quantum group C q [ SL 2 ], using a recent frame bundle...
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On the Noncommutative Geometry of Twisted Spheres
We describe noncommutative geometric aspects of twisted deformations, in particular of the spheres of Connes and Landi and of Connes and Dubois...
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More Noncommutative 4-Spheres
New examples of noncommutative 4-spheres are introduced.
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Noncommutative 4-Spheres Based on all Podleś 2-Spheres and Beyond
A wide class of noncommutative spaces, including 4-spheres based on all the quantum 2-spheres and suspensions of matrix quantum groups is described....
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Cyclic Cohomology and Hopf Algebra Symmetry
Cyclic cohomology has been recently adapted to the treatment of Hopf symmetry in noncommutative geometry. The resulting theory of characteristic...