Journal ArticleDOI
Deforming Maps for Quantum Algebras
TLDR
In this article, the authors find explicit functionals that map SU(2) algebra generators to those of several quantum deformations of that algebra, as well as their SU(1, 1) analogs.About:
This article is published in Physics Letters B.The article was published on 1990-06-28. It has received 322 citations till now. The article focuses on the topics: Algebra representation & Current algebra.read more
Citations
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Deformations of Lie Algebras using σ-Derivations
TL;DR: In this paper, an approach to deformations of the Witt and Virasoro algebras based on sigma-derivations was developed, and a theory of central extensions was developed for the q-deformations of these deformations.
Journal ArticleDOI
A (p, q)-oscillator realization of two-parameter quantum algebras
TL;DR: In this paper, a quantum algebra sup,q(2) with two independent deformation parameters (p, q) is studied, and the standard single-parameter (q) deformations are obtained in the limit p=q.
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On the q oscillator and the quantum algebra suq(1,1)
P. P. Kulish,E. V. Damaskinsky +1 more
TL;DR: In this paper, different q bosonisations of the quantum suq(1,1) algebra are given and the corresponding infinite dimensional representations of discrete series are analysed, and some problems of the q-deformed harmonic oscillator are discussed.
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Quasi-hom-Lie algebras, central extensions and 2-cocycle-like identities
Daniel Larsson,Sergei Silvestrov +1 more
TL;DR: Hartwig and Larsson as mentioned in this paper introduced the notion of a quasi-hom-Lie algebra, or simply, a qhl-algebra, which is a natural generalization of hom-Lie algebras introduced in a previous paper.
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Quantum groups and their applications in nuclear physics
Dennis Bonatsos,C. Daskaloyannis +1 more
TL;DR: In this article, a self-contained introduction to the necessary mathematical tools (q-numbers, q-analysis and q-oscillators), the suq(2) rotator model and its extensions, the construction of deformed exactly soluble models (u(3)so(3), model, Interacting Boson Model, Moszkowski model), the 3-dimensional q-deformed harmonic oscillator imd its relation to the nuclear shell model, and the symmetries of the anisotropic quantum harmonic oscillators with rational ratios of frequencies.
References
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Journal ArticleDOI
A q -difference analogue of U(g) and the Yang-Baxter equation
TL;DR: Aq-difference analogue of the universal enveloping algebra U(g) of a simple Lie algebra g is introduced in this article, and its structure and representations are studied in the simplest case g=sl(2).
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A q-analogue of U(g[(N+1)), Hecke algebra, and the Yang-Baxter equation
TL;DR: In this article, the structure and representations of the universal enveloping algebra U(g) were studied for g = g[(N+1) the structure of the algebra Ŭ(g), a q-analogue of the Universal Enveloping Algebra (U(g)).
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Twisted SU (2) group. An example of a non-commutative differential calculus
TL;DR: In this paper, a C*-algebre A engendree par deux elements α et γ satisfaisant une relation de commutation simple dependante de ν is presented.
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Finite-dimensional representations of the quantum analog of the enveloping algebra of a complex simple Lie algebra
TL;DR: In this paper, it was shown that all finite dimensional representations of the quantum analog of simple Lie algebras are completely reducible, and the irreducible representations can be seen as deformations of the representation of the classical (classical) Lie algebra.