*-Structures on Braided Spaces

Abstract

$\ast$-structures on quantum and braided spaces of the type defined via an R-matrix are studied. These include $q$-Minkowski and $q$-Euclidean spaces as additive braided groups. The duality between the $\ast$-braided groups of vectors and covectors is proved and some first applications to braided geometry are made.

20 pages

References in corpus (10)

• Braided Momentum Structure of the q-Poincare Group
• Algebraic {$q$}-Integration and Fourier Theory on Quantum and Braided Spaces
• Free Braided Differential Calculus, Braided Binomial Theorem and the Braided Exponential Map
• q-Euclidean space and quantum group wick rotation by twisting
• Introduction to Braided Geometry and $q$-Minkowski Space
• Reality in the Differential Calculus on q-euclidean Spaces
• Braided Matrix Structure of $q$-Minkowski Space and $q$-Poincare Group
• The $S{O}_q(N,\mathbf{R})$-Symmetric Harmonic Oscillator on the Quantum Euclidean Space ${\mathbf{R}}_q^N$ and its Hilbert Space Structure
• q-Epsilon tensor for quantum and braided spaces
• Wave Equations on q-Minkowski space

Cited by in corpus (15)

• Quantum Groups and Noncommutative Geometry
• Introduction to Braided Geometry and $q$-Minkowski Space
• Analysis on q-deformed quantum spaces
• q-Translations on quantum spaces
• Meaning of Noncommutative Geometry and the Planck-Scale Quantum Group
• Braided Geometry of the Conformal Algebra
• Quasi-Hopf $\ast$-Algebras
• Some remarks on the {$q$}-Poincare algebra in R-matrix form
• Many Q-Particles from One: A New Approach to $\ast$-Hopf Algebras?
• Bar categories and star operations
• Momentum and Position Representations for the q-deformed Euclidean Quantum Space
• Quasi-{$\ast$} Structure on {$q$}-Poincare algebras
• Quantum kinematics on q-deformed quantum spaces II, Wave functions on position and momentum space
• Quantum kinematics on q-deformed quantum spaces I, Mathematical Framework
• A new algebra which transmutes to the braided algebra