Mathematics – Quantum Algebra
Scientific paper
1995-02-20
Mathematics
Quantum Algebra
LATEX 33 pages. Mostly review. To appear in some version in a conference proceedings. Proposition~8.1 about $*$ structures was
Scientific paper
The braided approach to q-deformation (due to the author and collaborators) gives natural algebras $R_{21}u_1Ru_2=u_2R_{21}u_1R$ and $R_{21}x_1x_2=x_2x_1R$ 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 Poincar\'e 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 Poincar\'e quantum group $*$-structure and the dilaton problem are discussed.
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