Braided momentum in the q-Poincaré group

1992/10/27 by Shahn Majid, S. Majid · 8 citations
Mathematics · Physics and Astronomy · #Advanced Algebra and Geometry #Algebraic structures and combinatorial models #Black Holes and Theoretical Physics #hep-th

paper · pdf · doi:10.1063/1.530154

published as J.Math.Phys. 34 (1993) 2045-2058 · 22 pages, LATEX

arxiv created 1992/10/27 · openalex publication_date 1993/05/01 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

The q-Poincaré group of M. Schlieker et al. [Z. Phys. C 53, 79 (1992)] is shown to have the structure of a semidirect product and coproduct B× SOq(1,3) where B is a braided-quantum group structure on the q-Minkowski space of four-momentum with braided-coproduct Δ_p=p⊗1+1⊗p. Here the necessary B is not a usual kind of quantum group, but one with braid statistics. Similar braided vectors and covectors V(R′), V*(R′) exist for a general R-matrix. The abstract structure of the q-Lorentz group is also studied.

Citations

• Quantum R-matrices and factorization problems
• The Quantum Double as Quantum Mechanics

Cited by

• On the addition of quantum matrices
• Quantum and braided diffeomorphism groups
• Reflection equations andq-Minkowski space algebras
• Braided matrix structure ofq-Minkowski space andq-Poincar� group
• LocalD=4field theory onκ-deformed Minkowski space
• On the physical contents of q-deformed Minkowski spaces
• κ-DEFORMED POINCARÉ ALGEBRAS AND QUANTUM CLIFFORD–HOPF ALGEBRAS
• Quantum group covariant (anti)symmetrizers, -tensors, vielbein, Hodge map and Laplacian