Duality Principle and Braided Geometry

Abstract

We give an overview of a new kind symmetry in physics which exists between observables and states and which is made possible by the language of Hopf algebras and quantum geometry. It has been proposed by the author as a feature of Planck scale physics. More recent work includes corresponding results at the semiclassical level of Poisson-Lie groups and at the level of braided groups and braided geometry.

24 pages

References in corpus (11)

• Bicrossproduct structure of $\kappa$-Poincare group and non-commutative geometry
• Braided Momentum Structure of the q-Poincare Group
• Algebraic {$q$}-Integration and Fourier Theory on Quantum and Braided Spaces
• Quantum and Braided Linear Algebra
• Free Braided Differential Calculus, Braided Binomial Theorem and the Braided Exponential Map
• Quantum and Braided Lie Algebras
• Introduction to Braided Geometry and $q$-Minkowski Space
• Braided Matrix Structure of $q$-Minkowski Space and $q$-Poincare Group
• Quantum Random Walks and Time Reversal
• q-Epsilon tensor for quantum and braided spaces
• On the Addition of Quantum Matrices

Cited by in corpus (3)

• Quantum Groups and Noncommutative Geometry
• Noncommutative Model with Spontaneous Time Generation and Planckian bound
• On the semiduals of local isometry groups in 3d gravity