2008

q-Deformation and Semidualisation in 3d Quantum Gravity

Majid, S, Schroers, B J

Understand

We explore in detail the role in euclidean 3d quantum gravity of quantum Born reciprocity or `semidualisation'.

The latter is an algebraic operation defined using quantum group methods that interchanges position and momentum.
Using this we are able to clarify the structural relationships between the effective non-commutative geometries that have been discussed in the context of 3d gravity.
We show that the spin model based on D(U(su_2)) for quantum gravity without cosmological constant is the semidual of a quantum particle on a three-sphere, while the bicrossproduct (DSR) model is the semidual of a quantum particle on hyperbolic space.

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Then

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Closest in time.
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C. Meusburger and B. J. Schroers, · 2009
Closest in time.

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