Twisted Classical Poincaré Algebras

Abstract

We consider the twisting of Hopf structure for classical enveloping algebra $U(\hat{g})$, where $\hat{g}$ is the inhomogenous rotations algebra, with explicite formulae given for $D=4$ Poincaré algebra $(\hat{g}={\mathcal{P}}_4).$ The comultiplications of twisted $U^F({\mathcal{P}}_4)$ are obtained by conjugating primitive classical coproducts by $F\in U(\hat{c})\otimes U(\hat{c}),$ where $\hat{c}$ denotes any Abelian subalgebra of ${\mathcal{P}}_4$, and the universal $R-$matrices for $U^F({\mathcal{P}}_4)$ are triangular. As an example we show that the quantum deformation of Poincaré algebra recently proposed by Chaichian and Demiczev is a twisted classical Poincaré algebra. The interpretation of twisted Poincaré algebra as describing relativistic symmetries with clustered 2-particle states is proposed.

\Large \bf 19 pages, Bonn University preprint, November 1993

References in corpus (2)

• Braided Momentum Structure of the q-Poincare Group
• Quantum and Braided Linear Algebra

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