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Lledó, M. A.; Varadarajan, V. S.

doi:10.1023/a:1007498803198

Cited by 24 publications

(6 citation statements)

References 10 publications

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“…The second one points towards the well-known connection between Manin triples and the non-Abelian version of Poisson-Lie T -dual σ-models (see [69,[79][80][81][82][83][84] and references therein). We recall that these σ-models for four-dimensional DDs were constructed in [69], and among them we can find the two ones corresponding to our Cases 0 and 1 for the centrally extended (1 + 1) Poincaré group.…”

Section: Discussionmentioning

confidence: 97%

The Poincaré group as a Drinfel’d double

Ballesteros¹,

Gutiérrez-Sagredo²,

Herranz³

2018

Class. Quantum Grav.

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The eight nonisomorphic Drinfel'd double (DD) structures for the Poincaré Lie group in (2+1) dimensions are explicitly constructed in the kinematical basis. Also, the two existing DD structures for a non-trivial central extension of the (1+1) Poincaré group are also identified and constructed, while in (3+1) dimensions no Poincaré DD structure does exist. Each of the DD structures here presented has an associated canonical quasitriangular Poincaré r-matrix whose properties are analysed. Some of these r-matrices give rise to coisotropic Poisson homogeneous spaces with respect to the Lorentz subgroup, and their associated Poisson Minkowski spacetimes are constructed. Two of these (2+1) noncommutative DD Minkowski spacetimes turn out to be quotients by a Lorentz Poisson subgroup: the first one corresponds to the double of sl(2) with trivial Lie bialgebra structure, and the second one gives rise to a quadratic noncommutative Poisson Minkowski spacetime. With these results, the explicit construction of DD structures for all Lorentzian kinematical groups in (1+1) and (2+1) dimensions is completed, and the connection between (anti-)de Sitter and Poincaré r-matrices through the vanishing cosmological constant limit is also analysed.

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Section: Discussionmentioning

confidence: 97%

The Poincaré group as a Drinfel’d double

Ballesteros¹,

Gutiérrez-Sagredo²,

Herranz³

2018

Class. Quantum Grav.

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“…Our example will be based on the 6-dim Drinfeld double considered in [12,16,25], which we first review by following [12]. 7 It is just the non-compact group SO(3, 1) with G = SU(2) and dual G = E 3 = solv(SO(3, 1)) given by the Iwasawa decomposition of SO(3, 1) [26].…”

Section: The Drinfeld Doublementioning

confidence: 99%

Duality-invariant class of two-dimensional field theories

Sfetsos

1999

Nuclear Physics B

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We construct a new class of two-dimensional field theories with target spaces that are finite multiparameter deformations of the usual coset G/H-spaces. They arise naturally, when certain models, related by Poisson-Lie T-duality, develop a local gauge invariance at specific points of their classical moduli space. We show that canonical equivalences in this context can be formulated in loop space in terms of parafermionic-type algebras with a central extension. We find that the corresponding generating functionals are non-polynomial in the derivatives of the fields with respect to the space-like variable. After constructing models with three- and two-dimensional targets, we study renormalization group flows in this context. In the ultraviolet, in some cases, the target space of the theory reduces to a coset space or there is a fixed point where the theory becomes free

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“…In other words, (1.8) is a sub-Poisson coalgebra of the full canonical Poisson-Lie structure on the Drinfeld double D ns (su(2)) associated to the non-standard quantum deformation of sl(2) (as a real Lie group, D ns (su(2)) was proven to be isomorphic to a (2+1)D Poincaré group [19]). Since σ-models related by Poisson-Lie T-duality are directly connected to canonical Poisson-Lie structures on Drinfel'd doubles [20,21,22,23], the construction of the σ-model associated to D ns (su(2)) and its relationship with the results here presented could be worth to be considered.…”

Section: )mentioning

confidence: 96%

Curvature from quantum deformations

2005

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A Poisson coalgebra analogue of a (non-standard) quantum deformation of sl(2) is shown to generate an integrable geodesic dynamics on certain 2D spaces of non-constant curvature. Such a curvature depends on the quantum deformation parameter z and the flat case is recovered in the limit z\to 0. A superintegrable geodesic dynamics can also be defined in the same framework, and the corresponding spaces turn out to be either Riemannian or relativistic spacetimes (AdS and dS) with constant curvature equal to z. The underlying coalgebra symmetry of this approach ensures the existence of its generalization to arbitrary dimension.Comment: 10 pages, LaTe

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Abstract: Poisson-Lie target space duality is a framework where duality transformations are properly defined. In this letter we investigate the dual pair of σ-models defined by the double SO(3,1) in the Iwasawa decomposition. *

Cited by 24 publications

References 10 publications

The Poincaré group as a Drinfel’d double

The Poincaré group as a Drinfel’d double

Duality-invariant class of two-dimensional field theories

Curvature from quantum deformations

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