Reality in the Differential Calculus on q-euclidean Spaces

Abstract

The nonlinear reality structure of the derivatives and the differentials for the euclidean q-spaces are found. A real Laplacian is constructed and reality properties of the exterior derivative are given.

10 pages

Cited by in corpus (23)

• Field Theory on the q-deformed Fuzzy Sphere I
• Group Theoretical Foundations of Fractional Supersymmetry
• *-Structures on Braided Spaces
• The Euclidean Hopf algebra $U_q(e^N)$ and its fundamental Hilbert space representations
• Quantum group covariant (anti)symmetrizers, epsilon-tensors, vielbein, Hodge map and Laplacian
• Realization of $U_q(so(N))$ within the differntial algebra on ${\mathbf{R}}_q^N$
• Drinfel'd Twist and q-Deforming Maps for Lie Group Covariant Heisenberg Algebras
• Integration on quantum Euclidean space and sphere in $N$ dimensions
• Quantum groups and deformed special relativity
• Braided Chains of q-Deformed Heisenberg Algebrae
• The Geometry of the Quantum Euclidean Space
• Analysis on q-deformed quantum spaces
• A $q$-deformation of the Coulomb Problem
• On the deformability of Heisenberg algebras
• Phase spaces related to standard classical $r$-matrices
• q-Deformed su(2) instantons by q-quaternions
• q-Quaternions and q-deformed su(2) instantons
• Generalized Q-Exponentials Related to Orthogonal Quantum Groups and Fourier Transformations of Noncommutative Spaces
• On the hermiticity of q-differential operators and forms on the quantum Euclidean spaces R_q^N
• The Fourier Transform on Quantum Euclidean Space
• q-Deformed quaternions and su(2) instantons
• Hilbert Space Representation of an Algebra of Observables for q-Deformed Relativistic Quantum Mechanics
• The Hidden Geometry of the Quantum Euclidean Space