Journal ArticleDOI
A q-analogue of U(g[(N+1)), Hecke algebra, and the Yang-Baxter equation
TLDR
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)).Abstract:
We study for g=g[(N+1) the structure and representations of the algebra Ŭ(g), a q-analogue of the universal enveloping algebra U(g). Applying the result, we construct trigonometric solutions of the Yang-Baxter equation associated with higher representations of g.read more
Citations
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The symmetric q-oscillator algebra: q-coherent states, q-Bargmann–Fock realization and continuous q-Hermite polynomials with 0 < q < 1
H. Fakhri,A. Hashemi +1 more
TL;DR: In this paper, the symmetric q-analysis is used to construct a type of minimum-uncertainty q-coherent states in the Fock representation space of symmetric Q-oscillator ∗-algebra with 0 < q < 1.
Journal ArticleDOI
Quantum Dynamics of a Damped Deformed Oscillator
TL;DR: In this article, the interaction of a quantum deformed oscillator with the environment was studied, deriving a master equation whose form strongly depends on the type of deformation. But the authors did not consider the effects of the deformation on the oscillator's behavior.
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The q-deformed Dirac oscillator in the presence of a magnetic field in (1+2)-dimensions in Noncommutative phase space
TL;DR: In this paper, the eigenvalues of a q-deformed Dirac oscillator in (1+2)-dimensions in the presence of a magnetic field in a noncommutative phase space formalism are discussed.
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Duality and Multiplicative Stochastic Processes on Quantum Groups
TL;DR: In this paper, an analogue of McKean's stochastic product integral is introduced and used to define quantum processes with independent increments on quantum groups, which satisfy generalized Feynman-Kac type formulas and polynomial solutions of associated evolution equations are introduced in the form of Appell systems.
References
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Book
Groupes et algèbres de Lie
TL;DR: Les Elements de mathematique de Nicolas Bourbaki ont pour objet une presentation rigoureuse, systematique et sans prerequis des mathematiques depuis leurs fondements as mentioned in this paper.
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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).
Journal ArticleDOI
Some Exact Results for the Many-Body Problem in one Dimension with Repulsive Delta-Function Interaction
TL;DR: In this paper, the ground-state problem of spin-textonehalf{} fermions is reduced to a generalized Fredholm equation, in a generalized form, by using Bethe's hypothesis.
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Yang-baxter equation and representation theory: i
TL;DR: In this article, the problem of constructing the GL(N,ℂ) solutions to the Yang-Baxter equation (factorizedS-matrices) is considered.