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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Quantum groups, gravity, and the generalized uncertainty principle.
TL;DR: The result indicates that in the $\ensuremath{\kappa}$-deformed Poincar\'e algebra a minimal observable length emerges naturally.
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Quantum deformations of certain simple modules over enveloping algebras
TL;DR: Soit F un corps. Soit F 0 un sous-corps de F. On montre qu'un module integrable de poids le plus eleve V de U admet une deformation quantique as discussed by the authors.
Journal ArticleDOI
Form factors of the xxz heisenberg spin-1/2 finite chain
TL;DR: In this paper, the form factors for local spin operators of the XXZ Heisenberg spin-z finite chain are computed in terms of expectation values (in ferromagnetic reference state) of the operator entries of the quantum monodromy matrix satisfying Yang-Baxter algebra.
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Q -analogues of Clifford and Weyl algebras-spinor and oscillator representations of quantum enveloping algebras
TL;DR: In this article, spinor and oscillator representations of quantum enveloping algebras of typeAN−1,BN,CN,DN and AN−1(1) were constructed.
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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.
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.