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

1995/02/20 by Shahn Majid, Majid, S.
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Black Holes and Theoretical Physics #Advanced Algebra and Geometry

paper · pdf · doi:10.48550/arxiv.q-alg/9502014

Abstract

The braided approach to q-deformation (due to the author and collaborators) gives natural algebras R₂₁u₁Ru₂=u₂R₂₁u₁R and R₂₁x₁x₂=x₂x₁R 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 *-structure and the dilaton problem are discussed.

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