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On the q-quantum gravity loop algebra

Seth Major

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A class of deformations of the q-quantum gravity loop algebra is shown to be incompatible with the combinatorics of Temperley–Lieb recoupling theory at a root of unity. This incompatibility appears to extend to more general deformation parameters.


PACS

04.60.Pp Loop quantum gravity, quantum geometry, spin foams

98.80.Es Observational cosmology (including Hubble constant, distance scale, cosmological constant, early Universe, etc)

98.80.Qc Quantum cosmology

02.10.-v Logic, set theory, and algebra

MSC

83C45 Quantization of the gravitational field

81Rxx Groups and algebras in quantum theory

83F05 Cosmology

Subjects

Mathematical physics

Gravitation and cosmology

Astrophysics and astroparticles

Dates

Issue 6 (21 March 2008)

Received 30 August 2007, in final form 10 January 2008

Published 4 March 2008



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