Quantum (2+1) kinematical algebras: a global approach

Ballesteros, Ángel; Herranz, Francisco J.; Olmo, M. A. del; Santander, Mariano

doi:10.1088/0305-4470/27/4/021

Cited by 56 publications

(136 citation statements)

References 22 publications

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“…If the cocommutator is written as: 19) then the dual bracket is (first order in w and linear in the generators): 20) plus, in general, higher order terms both in w and in the generators. Therefore, these three sets of fundamental bialgebras give rise to bialgebras whose "linearized" dual algebras are characterized by the brackets given in table II.…”

Section: Hopf Algebra Contractions Of U Z So(3)mentioning

confidence: 99%

“…Among them, the Hopf structure of (g (κ 1 ,κ 2 ,κ 3 ) , δ (1,1,1) 03,12 ) has been studied in [19]; the particular cases (U w g (−1,−1,1) , ∆ 03,12 ) (so(3, 1) q ) and (U w g (0,1,1) , ∆ 03,12 ) (e(3) q ) have been given in [29] and [30], respectively. We shall explicitly discuss two examples containing non-coboundary objects, since they provide new quantizations of some interesting algebras.…”

Section: Hopf Algebra Contractions Of U Z So(4)mentioning

confidence: 99%

“…In this way we can explore the differences underlying these contractions from a physical point of view. In particular, by assuming the standard kinematical assignation [19]:…”

Section: Quantum (2+1) Poincaré and Galilei Algebrasmentioning

confidence: 99%

“…Both (U w g (0,−1,1) , ∆ 02,13 ) and (U w g (0,−1,1) , ∆ 03,12 ) were studied in [19], and can be interpreted as relativistic symmetries with a discretized spatial direction. .10)).…”

Section: Quantum (2+1) Poincaré and Galilei Algebrasmentioning

confidence: 99%

“…These coboundary deformations are connected with the first class of quantum Poincaré algebras and were studied in [19].…”

Section: Quantum (2+1) Poincaré and Galilei Algebrasmentioning

confidence: 99%

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Lie bialgebra contractions and quantum deformations of quasi-orthogonal algebras

Ballesteros

Gromov

Herranz

et al. 1995

Journal of Mathematical Physics

112

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Lie bialgebra contractions are introduced and classified. A non-degenerate coboundary bialgebra structure is implemented into all pseudo-orthogonal algebras so(p, q) starting from the one corresponding to so(N + 1). It allows to introduce a set of Lie bialgebra contractions which leads to Lie bialgebras of quasi-orthogonal algebras. This construction is explicitly given for the cases N = 2, 3, 4. All Lie bialgebra contractions studied in this paper define Hopf algebra contractions for the Drinfel'd-Jimbo deformations U z so(p, q). They are explicitly used to generate new non-semisimple quantum algebras as it is the case for the Euclidean, Poincaré and Galilean algebras.

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Section: Hopf Algebra Contractions Of U Z So(3)mentioning

confidence: 99%

Section: Hopf Algebra Contractions Of U Z So(4)mentioning

confidence: 99%

“…In this way we can explore the differences underlying these contractions from a physical point of view. In particular, by assuming the standard kinematical assignation [19]:…”

Section: Quantum (2+1) Poincaré and Galilei Algebrasmentioning

confidence: 99%

Section: Quantum (2+1) Poincaré and Galilei Algebrasmentioning

confidence: 99%

“…These coboundary deformations are connected with the first class of quantum Poincaré algebras and were studied in [19].…”

Section: Quantum (2+1) Poincaré and Galilei Algebrasmentioning

confidence: 99%

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