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arXiv · 1312.5690

The geometry of quantum lens spaces: real spectral triples and bundle structure

Andrzej Sitarz·Jan Jitse Venselaar
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Abstract

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 quantum group $SU_q(2)$. These spectral triples are given by weakening some of the conditions of a real spectral triple. We classify the irreducible almost real spectral triples on quantum lens spaces and we study unitary equivalences of such quantum lens spaces. Applying a useful characterization of principal $U(1)$-fibrations in noncommutative geometry, we show that all such quantum lens spaces are principal $U(1)$-fibrations over quantum teardrops.

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Andrzej Sitarz, Jan Jitse Venselaar. 2015-02-27. The geometry of quantum lens spaces: real spectral triples and bundle structure. https://doi.org/10.1007/s11040-015-9179-4

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