A *-product on SL(2) and the corresponding nonstandard $$(\mathfrak{s}\mathfrak{l}({\text{2}}))$$

Ohn, Christian

doi:10.1007/bf00398304

Cited by 128 publications

(106 citation statements)

References 3 publications

Supporting

Mentioning

106

Contrasting

Order By: Relevance

“…In this situation, N can be defined in terms of A + and A − by using the Casimir (4.22). In general, this type of non-standard deformed bosons can be expected to build up q-boson realizations of the already known non-standard quantum algebras [17,18].…”

Section: Determine a Hopf Algebra (Denoted By U (N)mentioning

confidence: 99%

Lie bialgebra quantizations of the oscillator algebra and their universalR-matrices

Ballesteros¹,

Herranz²

1996

J. Phys. A: Math. Gen.

View full text Add to dashboard Cite

show abstract

Section: Determine a Hopf Algebra (Denoted By U (N)mentioning

confidence: 99%

Lie bialgebra quantizations of the oscillator algebra and their universalR-matrices

Ballesteros¹,

Herranz²

1996

J. Phys. A: Math. Gen.

View full text Add to dashboard Cite

show abstract

“…In the limit α → 0 we obtain for the R-matrix (5.30) We add that the Jordanian deformation has been described as well in a deformed sl(2; R) algebra basis [47][48][49].…”

Section: Explicit Isomorphism Between Su(1 1) and Sl(2; R) Bialgebramentioning

confidence: 99%

Quantizations of $$D=3$$ D = 3 Lorentz symmetry

Lukierski

Tolstoy

2017

Eur. Phys. J. C

View full text Add to dashboard Cite

Using the isomorphism o(3; C) sl(2; C) we develop a new simple algebraic technique for complete classification of quantum deformations (the classical r -matrices) for real forms o(3) and o(2, 1) of the complex Lie algebra o(3; C) in terms of real forms of sl(2; C): su(2), su(1, 1) and sl(2; R). We prove that the D = 3 Lorentz symmetry o(2, 1) su(1, 1) sl(2; R) has three different Hopfalgebraic quantum deformations, which are expressed in the simplest way by two standard su(1, 1) and sl(2; R) qanalogs and by simple Jordanian sl(2; R) twist deformation. These quantizations are presented in terms of the quantum Cartan-Weyl generators for the quantized algebras su(1, 1) and sl(2; R) as well as in terms of quantum Cartesian generators for the quantized algebra o(2, 1). Finally, some applications of the deformed D = 3 Lorentz symmetry are mentioned.

show abstract

“…The proof is based on the fact that, for any choice of the function H, the Hamiltonian H (N ) z has a deformed Poisson coalgebra symmetry, sl z (2, R), coming (under a certain symplectic realization) from the non-standard quantum deformation of sl(2, R) [38,39] where z is the deformation parameter (q = e z ). If we perform the limit z → 0 in all the results given in Theorem 2, we shall exactly recover Theorem 1.…”

Section: The Proofmentioning

confidence: 99%

Quantum Deformations and Superintegrable Motions on Spaces with Variable Curvature

Ragnisco

Ballesteros

Herranz

et al. 2007

SIGMA

View full text Add to dashboard Cite

Abstract. An infinite family of quasi-maximally superintegrable Hamiltonians with a common set of (2N − 3) integrals of the motion is introduced. The integrability properties of all these Hamiltonians are shown to be a consequence of a hidden non-standard quantum sl(2, R) Poisson coalgebra symmetry. As a concrete application, one of this Hamiltonians is shown to generate the geodesic motion on certain manifolds with a non-constant curvature that turns out to be a function of the deformation parameter z. Moreover, another Hamiltonian in this family is shown to generate geodesic motions on Riemannian and relativistic spaces all of whose sectional curvatures are constant and equal to the deformation parameter z. This approach can be generalized to arbitrary dimension by making use of coalgebra symmetry.

show abstract

A *-product on SL(2) and the corresponding nonstandard $$(\mathfrak{s}\mathfrak{l}({\text{2}}))$$

Cited by 128 publications

References 3 publications

Lie bialgebra quantizations of the oscillator algebra and their universalR-matrices

Lie bialgebra quantizations of the oscillator algebra and their universalR-matrices

Quantizations of $$D=3$$ D = 3 Lorentz symmetry

Quantum Deformations and Superintegrable Motions on Spaces with Variable Curvature

Contact Info

Product

Resources

About