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
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Exact analytical expression for magnetoresistance using quantum groups
S. A. Alavi,Shahin Rouhani +1 more
TL;DR: In this article, an exact analytical expression for magnetoresistance using noncommutative geometry and quantum groups was obtained, from which the quantum interpretation of the quantum corrections to the conductivity was explained.
Journal ArticleDOI
Graded contractions and bicrossproduct structure of deformed inhomogeneous algebras
TL;DR: In this paper, a family of deformed Hopf algebras corresponding to the classical maximal isometry algesas of zero-curvature N-dimensional spaces (the inhomogeneous algesbras, p + q = N, as well as some of their contractions) are shown to have a bicrossproduct structure.
Journal ArticleDOI
Algebraic structures and eigenstates for integrable collective field theories
Jean Avan,Antal Jevicki +1 more
TL;DR: In this article, conditions for the construction of polynomial eigen-operators for the Hamiltonian of collective string field theories are explored, and a Lie algebra is constructed for one monomial potentialv(x)=μxcffff2+g/x��2 in the collective field theory.
Journal ArticleDOI
Boson representations, non-standard quantum algebras and contractions
TL;DR: In this paper, a Gelfan'd-Dyson mapping is used to generate a one-boson realization for the non-standard quantum deformation of which directly provides its infinite-and finite-dimensional irreducible representations.
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Thermostatistics of the multi-dimensional q-deformed fermionic Newton oscillators
Abdullah Algin,Emine Arslan +1 more
TL;DR: In this article, the high and low-temperature thermostatistical properties of a gas of the multi-dimensional q-deformed fermionic Newton oscillators are obtained.
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.
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.