scholarly journals HODGE DUALITY OPERATORS ON LEFT-COVARIANT EXTERIOR ALGEBRAS OVER TWO- AND THREE-DIMENSIONAL QUANTUM SPHERES

2013 ◽  
Vol 25 (05) ◽  
pp. 1350009 ◽  
Author(s):  
ALESSANDRO ZAMPINI
Keyword(s):  
Three Dimensional ◽  
Exterior Algebra ◽  
Symmetric Tensors ◽  
Quantum Sphere ◽  
Quantum Spheres

Using non-canonical braidings, we first introduce a notion of symmetric tensors and corresponding Hodge operators on a class of left-covariant 3d differential calculi over SU q(2), then we induce Hodge operators on the left-covariant 2d exterior algebra over the Podles quantum sphere.

A Hodge–de Rham Dirac operator on the quantum SU(2)

2018 ◽  
Vol 15 (02) ◽  
pp. 1850030 ◽  
Author(s):  
Fabio Di Cosmo ◽  
Giuseppe Marmo ◽  
Juan Manuel Pérez-Pardo ◽  
Alessandro Zampini
Keyword(s):  
Dirac Operator ◽  
Three Dimensional ◽  
Exterior Algebra ◽  
De Rham ◽  
Quantum Spheres

We describe how it is possible to define a Hodge–de Rham Dirac operator associated to a suitable Cartan-Killing metric form upon the exterior algebra over the quantum spheres [Formula: see text] equipped with a three-dimensional left covariant calculus.

scholarly journals EXAMPLES OF HODGE LAPLACIANS ON QUANTUM SPHERES

2012 ◽  
Vol 09 (02) ◽  
pp. 1260009 ◽  
Author(s):  
ALESSANDRO ZAMPINI
Keyword(s):  
Three Dimensional ◽  
Quantum Space ◽  
Quantum Spheres

Using a non-canonical braiding over the three-dimensional left covariant calculus we present a family of Hodge operators on SU q(2) and on its homogeneous quantum space [Formula: see text].

Eigenvalue Finding of Three-Dimensional Second-Order Real Symmetric Tensors

2012 ◽  
Vol 40 (3) ◽  
pp. 172-181
Author(s):  
E. Lucena Neto ◽  
A. L. Carvalho Neto ◽  
P. I. B. Queiroz
Keyword(s):  
Three Dimensional ◽  
Second Order ◽  
Symmetric Tensors

scholarly journals The quantum spheres and their embedding into quantum Minkowski space-time

2002 ◽  
Vol 2 (7) ◽  
pp. 315-335
Author(s):  
M. Lagraa
Keyword(s):  
Hilbert Space ◽  
Minkowski Space ◽  
Space Time ◽  
Time Coordinate ◽  
Quantum Sphere ◽  
Minkowski Space Time ◽  
Quantum Spheres

We recast the Podleś spheres in the noncommutative physics context by showing that they can be regarded as slices along the time coordinate of the different regions of the quantum Minkowski space-time. The investigation of the transformations of the quantum sphere states under the left coaction of theSOq(3)group leads to a decomposition of the transformed Hilbert space states in terms of orthogonal subspaces exhibiting the periodicity of the quantum sphere states.

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