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arXiv · hep-th/9312068

Twisted Classical Poincaré Algebras

Jerzy Lukierski·Henri Ruegg·Valerij N. Tolstoy·Anatol Nowicki
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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 $(\hat{g}={\cal P}_4).$ The comultiplications of twisted $U^F({\cal P}_4)$ 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 ${\cal P}_4$, and the universal $R-$matrices for $U^F({\cal P}_4)$ 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.

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Jerzy Lukierski, Henri Ruegg, Valerij N. Tolstoy, Anatol Nowicki. 1993-12-09. Twisted Classical Poincaré Algebras. https://doi.org/10.1088/0305-4470%2F27%2F7%2F018

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