κ-DEFORMED POINCARÉ ALGEBRAS AND QUANTUM CLIFFORD–HOPF ALGEBRAS

2008/01/31 by Roldao da Rocha, ROLDÃO DA ROCHA, Alex E. Bernardini +3
Mathematics · Physics and Astronomy · #Advanced Operator Algebra Research #Algebra over a field #Algebra representation #Algebraic and Geometric Analysis #Algebraic structures and combinatorial models #Cellular algebra #Clifford algebra #Current algebra #Filtered algebra #Quantum affine algebra #Quantum algebra #Quantum group #Subalgebra #math-ph #math.MP #msc:15A66 #msc:16W30 #msc:20G42

paper · pdf · doi:10.1142/s0219887810004567

published as Int.J.Geom.Meth.Mod.Phys. 7 (2010) 821-836 · 10 pages, RevTeX, one Section and references added, improved content.

arxiv created 2010/04/01 · openalex publication_date 2010/08/01 · arxiv updated 2010/09/28 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

The Minkowski space–time quantum Clifford algebra structure associated with the conformal group and the Clifford–Hopf alternative κ-deformed quantum Poincaré algebra is investigated in the Atiyah–Bott–Shapiro mod 8 theorem context. The resulting algebra is equivalent to the deformed anti-de Sitter algebra [Formula: see text], when the associated Clifford–Hopf algebra is taken into account, together with the associated quantum Clifford algebra and a (not braided) deformation of the periodicity Atiyah–Bott–Shapiro theorem.

Citations

• THE κ-WEYL GROUP AND ITS ALGEBRA
• HIDDEN CONSEQUENCE OF ACTIVE LOCAL LORENTZ INVARIANCE
• Braided momentum in the q-Poincaré group
• Obtaining the equation of motion for a fermionic particle in a generalized Lorentz-violating system framework
• Isotopic Liftings of Clifford Algebras and Applications in Elementary Particle Mass Matrices
• A new “null-plane” quantum Poincaré algebra
• Classical and Quantum Mechanics of Free κ-Relativistic Systems
• Reflection equations andq-Minkowski space algebras
• Observer-independent quantum of mass