Twisted conformal algebra so(4, 2)

A new twisted deformation, Uz(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 Uz(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.