A Triangular Deformation of the two Dimensional Poincaré Algebra
نویسنده
چکیده
Contracting the h-deformation of SL(2, R), we construct a new deformation of two dimensional Poincaré algebra, the algebra of functions on its group and its differential structure. It is also shown that the Hopf algebra is triangular, and its universal R matrix is also constructed explicitly. Then, we find a deformation map for the universal enveloping algebra, and at the end, give the deformed mass shells and Lorentz transformation.
منابع مشابه
Non-standard quantum (1+1) Poincaré group: a T–matrix approach
The Hopf algebra dual form for the non–standard uniparametric deformation of the (1+1) Poincaré algebra iso(1, 1) is deduced. In this framework, the quantum coordinates that generate Funw(ISO(1, 1)) define an infinite dimensional Lie algebra. A change in the basis of the dual form is obtained in order to compare this deformation to the standard one. Finally, a non– standard quantum Heisenberg g...
متن کاملSolving a class of nonlinear two-dimensional Volterra integral equations by using two-dimensional triangular orthogonal functions
In this paper, the two-dimensional triangular orthogonal functions (2D-TFs) are applied for solving a class of nonlinear two-dimensional Volterra integral equations. 2D-TFs method transforms these integral equations into a system of linear algebraic equations. The high accuracy of this method is verified through a numerical example and comparison of the results with the other numerical methods.
متن کاملNonstandard Poincare and Heisenberg Algebras
New deformations of the Poincare group Fun(P (1 + 1)) and its dual enveloping algebra U(p(1 + 1)) are obtained as a contraction of the hdeformed (Jordanian) quantum group Fun(SLh(2)) and its dual. A nonstandard quantization of the Heisenberg algebra U(h(1)) is also investigated. Ref. SISSA: 85/96/FM Off late, considerable interest has been generated towards the nonstandard quantization of Lie g...
متن کاملCategory O over a Deformation of the Symplectic Oscillator Algebra
We discuss the representation theory of Hf , which is a deformation of the symplectic oscillator algebra sp(2n) ⋉ hn, where hn is the ((2n+1)-dimensional) Heisenberg algebra. We first look at a more general algebra with a triangular decomposition. Assuming the PBW theorem, and one other hypothesis, we show that the BGG category O is abelian, finite length, and self-dual. We decompose O as a dir...
متن کامل(Anti)de Sitter/Poincaré symmetries and representations from Poincaré/Galilei through a classical deformation approach
A classical deformation procedure, based on universal enveloping algebras, Casimirs and curvatures of symmetrical homogeneous spaces, is applied to several cases of physical relevance. Starting from the (3 + 1)D Galilei algebra, we describe at the level of representations the process leading to its two physically meaningful deformed neighbours. The Poincaré algebra is obtained by introducing a ...
متن کامل