TWISTED CLASSICAL POINCARE ALGEBRAS

We consider the twisting of the Hopf structure for the classical enveloping algebra U(g), where g is an inhomogeneous rotation algebra, with explicit formulae given for the D = 4 Poincare algebra (g = P4). The comultiplications of twisted U(F)(P4) are obtained by conjugating the primitive classical coproducts by F is-an-element-of U(c) X U(c), where c denotes any Abelian subalgebra of P4, and the universal R-matrices for U(F)(P4) are triangular. As an example we show that the quantum deformation of the Poincare algebra recently proposed by Chaichain and Demiczev is a twisted classical Poincare algebra. The interpretation of the twisted Poincare algebra as describing relativistic symmetries with clustered two-particle states is proposed.