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
More filters
Journal ArticleDOI
$C_{\lambda}$-extended harmonic oscillator and (para)supersymmetric quantum mechanics
C. Quesne,N. Vansteenkiste +1 more
TL;DR: In this article, a generalized deformed oscillator algebras with cyclic shape invariant potentials and a bosonization of PSSQM of order two is obtained.
Book ChapterDOI
Introduction to quantum groups
TL;DR: In this paper, an approach to quantum groups based on the quantization of Poisson-Lie groups is presented, and the quantum Yang-Baxter Equation and the algebraic definition of quantum groups appear quite naturally.
Journal ArticleDOI
A new current algebra and the reflection equation
Pascal Baseilhac,K. Shigechi +1 more
TL;DR: In this article, an explicit algebra isomorphism between the quantum reflection algebra for the R-matrix and a new type of current algebra was established, called q-Onsager algebras.
Journal ArticleDOI
Quantum algebraic structures compatible with the harmonic oscillator Newton equation
TL;DR: In this paper, the authors studied algebraic structures that are compatible with the quantization of the harmonic oscillator through its Newton equation, such as SU(2) Lie algebras and SUq(2), which appear in a variety of physical models.
Journal ArticleDOI
A relativistic relative of the magnon S-matrix
TL;DR: In this paper, a relativistic scattering theory based on a q deformation and large string tension limit of the magnon S-matrix of the string world sheet theory was constructed.
References
More filters
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.
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).
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.
Journal ArticleDOI
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.