Lie bialgebra contractions and quantum deformations of quasi‐orthogonal algebras

A. Ballesteros; N. A. Gromov; F. J. Herranz; M. A. del Olmo; M. Santander

doi:10.1063/1.531368

Lie bialgebra contractions and quantum deformations of quasi‐orthogonal algebras

Journal of Mathematical Physics ◽

10.1063/1.531368 ◽

1995 ◽

Vol 36 (10) ◽

pp. 5916-5937 ◽

Cited By ~ 31

Author(s):

A. Ballesteros ◽

N. A. Gromov ◽

F. J. Herranz ◽

M. A. del Olmo ◽

M. Santander

Keyword(s):

Lie Bialgebra ◽

Quantum Deformations

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Palatial Twistors from Quantum Inhomogeneous Conformal Symmetries and Twistorial DSR Algebras

Symmetry ◽

10.3390/sym13081309 ◽

2021 ◽

Vol 13 (8) ◽

pp. 1309

Author(s):

Jerzy Lukierski

Keyword(s):

Phase Space ◽

Hopf Algebras ◽

Deformation Parameter ◽

Heisenberg Algebra ◽

Planck Length ◽

Covariant Quantum ◽

Drinfeld Twist ◽

Quantum Deformations ◽

Heisenberg Double ◽

Conformal Symmetries

We construct recently introduced palatial NC twistors by considering the pair of conjugated (Born-dual) twist-deformed D=4 quantum inhomogeneous conformal Hopf algebras Uθ(su(2,2)⋉T4) and Uθ¯(su(2,2)⋉T¯4), where T4 describes complex twistor coordinates and T¯4 the conjugated dual twistor momenta. The palatial twistors are suitably chosen as the quantum-covariant modules (NC representations) of the introduced Born-dual Hopf algebras. Subsequently, we introduce the quantum deformations of D=4 Heisenberg-conformal algebra (HCA) su(2,2)⋉Hℏ4,4 (Hℏ4,4=T¯4⋉ℏT4 is the Heisenberg algebra of twistorial oscillators) providing in twistorial framework the basic covariant quantum elementary system. The class of algebras describing deformation of HCA with dimensionfull deformation parameter, linked with Planck length λp, is called the twistorial DSR (TDSR) algebra, following the terminology of DSR algebra in space-time framework. We describe the examples of TDSR algebra linked with Palatial twistors which are introduced by the Drinfeld twist and the quantization map in Hℏ4,4. We also introduce generalized quantum twistorial phase space by considering the Heisenberg double of Hopf algebra Uθ(su(2,2)⋉T4).

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