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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A Complete Formulation of the Baum–Connes Conjecture for the Action of Discrete Quantum Groups
Posted Content
On the Representation Theory of an Algebra of Braids and Ties
TL;DR: In this paper, the tensor space representation for the algebra ${\cal E}_n(u)$ introduced by F. Aicardi and J. Juyumaya as an abstraction of the Yokonuma-Hecke algebra was constructed.
Journal ArticleDOI
Universal integrability objects
TL;DR: In this paper, the main points of the quantum group approach in the theory of quantum integrable systems are discussed and a complete set of functional relations correcting inexactitudes of previous considerations are given.
Journal ArticleDOI
Higher Order Relations for ADE-Type Generalized q-Onsager Algebras
Pascal Baseilhac,Thu Thuy Vu +1 more
TL;DR: In this article, the fundamental generators of the generalized q-Onsager algebra were conjectured as deformed analogies of Lusztig's rth higher order higher order q-Serre relations associated with the generalized Q-OnSager algebra.
Journal ArticleDOI
Bicovariant differential calculus on the two‐parameter quantum group GLp,q(2)
Xiao‐Dong Sun,Shi‐Kun Wang +1 more
TL;DR: In this paper, the quantum Lie algebra and quantum de Rham complex of the two-parameter quantum group GLp,q(2) are presented and it is shown that the differential calculus on GLp is bicovariant.
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.
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.