q-Translations on quantum spaces

Abstract

Attention is focused on quantum spaces of particular importance in physics, i.e. two-dimensional quantum plane, q-deformed Euclidean space in three or four dimensions, and q-deformed Minkowski space. Each of these quantum spaces can be combined with its symmetry algebra to form a Hopf algebra. The Hopf structures on quantum space coordinates imply their translation. This article is devoted to the question how to calculate translations on the quantum spaces under consideration.

55 pages, Latex, more detailed introduction and conclusion, additional section about basic concepts, some modifications to improve clarity, typos corrected

References in corpus (7)

• The quantum structure of spacetime at the Planck scale and quantum fields
• On a Lorentz-Invariant Interpretation of Noncommutative Space-Time and Its Implications on Noncommutative QFT
• Quantum and Braided Linear Algebra
• Differential Calculus on Iso_q (N), Quantum Poincare' Algebra and q - Gravity
• Introduction to Braided Geometry and $q$-Minkowski Space
• *-Structures on Braided Spaces
• q-Integration on Quantum Spaces

Cited by in corpus (6)

• q-Deformed quantum Lie algebras
• Analysis on q-deformed quantum spaces
• Braided products for quantum spaces
• Non-relativistic Schroedinger theory on q-deformed quantum spaces I, Mathematical framework and equations of motion
• Quantum kinematics on q-deformed quantum spaces I, Mathematical Framework
• Quantum kinematics on q-deformed quantum spaces II, Wave functions on position and momentum space