Some remarks on the {$q$}-Poincare algebra in R-matrix form

Abstract

The braided approach to q-deformation (due to the author and collaborators) gives natural algebras $R_{21}{u}_{1}R{u}_2=u_2{R}_{21}{u}_{1}R$ and $R_{21}{x}_1{x}_2=x_2{x}_{1}R$ for q-Minkowski and q-Euclidean spaces respectively. These algebras are covariant under a corresponding background `rotation' quantum group. Semidirect product by this according to the bosonisation procedure (also due to the author) gives the corresponding Poincaré quantum groups. We review the construction and collect the resulting R-matrix formulae for both Euclidean and Minkowski cases in both enveloping algebra and function algebra form, and the duality between them. Axioms for the Poincaré quantum group $\ast$-structure and the dilaton problem are discussed.

LATEX 33 pages. Mostly review. To appear in some version in a conference proceedings. Proposition~8.1 about $\ast$ structures was extended.

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Cited by in corpus (1)

• Quantum Deformations of Conformal Algebras Introducing Fundamental Mass Parameters