2016
DOI: 10.1103/physrevd.94.084044
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Abstract: By applying loop quantum gravity techniques to 3D gravity with a positive cosmological constant Λ, we show how the local gauge symmetry of the theory, encoded in the constraint algebra, acquires the quantum group structure of so q (4), with q = exp (i ̵ h √ Λ 2κ). By means of an Inonu-Wigner contraction of the quantum group bi-algebra, keeping κ finite, we obtain the kappa-Poincaré algebra of the flat quantum space-time symmetries.

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Cited by 42 publications
(47 citation statements)
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“…Such noncommutative and/or discrete nature of quantum spacetime follows as well from loop quantum gravity (LQG) approach [4][5][6], where the discretization is dynamical, 1 based on the existence in LQG framework of minimal lengths, minimal area surfaces or minimal volume quanta. In particular recently by applying LQG techniques to the quantum deformation of D = 3 gravity with positive cosmological constant Λ it has been shown [7] that one gets the quantum symmetry of U q (o(4)), where ln q ∼ Λ, in analogy with earlier results of [8] and [9] for Lorentz signature.…”
Section: Jhep11(2017)187mentioning
confidence: 85%
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“…Such noncommutative and/or discrete nature of quantum spacetime follows as well from loop quantum gravity (LQG) approach [4][5][6], where the discretization is dynamical, 1 based on the existence in LQG framework of minimal lengths, minimal area surfaces or minimal volume quanta. In particular recently by applying LQG techniques to the quantum deformation of D = 3 gravity with positive cosmological constant Λ it has been shown [7] that one gets the quantum symmetry of U q (o(4)), where ln q ∼ Λ, in analogy with earlier results of [8] and [9] for Lorentz signature.…”
Section: Jhep11(2017)187mentioning
confidence: 85%
“…6 The symmetric part rs is g-invariant and in the case of semi-simple algebra is related to the so-called split Casimir (non-degenerate Cartan-Killing form). 7 The importance of quantum R-matrices follows from their applications as solutions of qYBE in various branches of theoretical physics e.g. conformal field theory, statistical mechanical models, and in mathematics, e.g.…”
Section: Jhep11(2017)187mentioning
confidence: 99%
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“…[53][54][55][56]. However, in previous treatments, it was a found as a consequence of the presence of group-valued constraints (moment maps).…”
Section: Jhep02(2017)061mentioning
confidence: 96%
“…• it makes transparent the Drinfel'd double algebra structure, which in past (loop quantum gravity) discussions was rather hidden in the algebra of constraints [55,56];…”
Section: Discussionmentioning
confidence: 99%