Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 10 (2014), 097, 13 pages      arXiv:1405.5396

Quantum Dimension and Quantum Projective Spaces

Marco Matassa
SISSA, Via Bonomea 265, I-34136 Trieste, Italy

Received July 29, 2014, in final form September 21, 2014; Published online September 25, 2014

We show that the family of spectral triples for quantum projective spaces introduced by D'Andrea and Dąbrowski, which have spectral dimension equal to zero, can be reconsidered as modular spectral triples by taking into account the action of the element $K_{2\rho}$ or its inverse. The spectral dimension computed in this sense coincides with the dimension of the classical projective spaces. The connection with the well known notion of quantum dimension of quantum group theory is pointed out.

Key words: quantum projective spaces; quantum dimension; modular spectral triples.

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