Twisted Conformal Algebra so(4,2)

Abstract

A new twisted deformation, U_z(so(4,2)), of the conformal algebra of the (3+1)-dimensional Minkowskian spacetime is presented. This construction is provided by a classical r-matrix spanned by ten Weyl-Poincare generators, which generalizes non-standard quantum deformations previously obtained for so(2,2) and so(3,2). However, by introducing a conformal null-plane basis it is found that the twist can indeed be supported by an eight-dimensional carrier subalgebra. By construction the Weyl-Poincare subalgebra remains as a Hopf subalgebra after deformation. Non-relativistic limits of U_z(so(4,2)) are shown to be well defined and they give rise to new twisted conformal algebras of Galilean and Carroll spacetimes. Furthermore a difference-differential massless Klein-Gordon (or wave) equation with twisted conformal symmetry is constructed through deformed momenta and position operators. The deformation parameter is interpreted as the lattice step on a uniform Minkowskian spacetime lattice discretized along two basic null-plane directions.

20 pages, LaTeX

References in corpus (4)

• κ-deformations of D=4 Weyl and conformal symmetries
• New quantum (anti)de Sitter algebras and discrete symmetries
• Extensions of Peripheric Extended Twists and Inhomogeneous Lie Algebras
• Quantization of Lie-Poisson structures by peripheric chains

Cited by in corpus (4)

• Three-dimensional gravity and Drinfel'd doubles: spacetimes and symmetries from quantum deformations
• Non-commutative relativistic spacetimes and worldlines from 2+1 quantum (anti-)de Sitter groups
• Discrete q-derivatives and symmetries of q-difference equations
• A new Doubly Special Relativity theory from a quantum Weyl-Poincare algebra