Quantum and braided diffeomorphism groups

Abstract

We develop a general theory of `quantum' diffeomorphism groups based on the universal comeasuring quantum group $M(A)$ associated to an algebra $A$ and its various quotients. Explicit formulae are introduced for this construction, as well as dual quasitriangular and braided R-matrix versions. Among the examples, we construct the $q$-diffeomorphisms of the quantum plane $yx=qxy$, and recover the quantum matrices $M_q(2)$ as those respecting its braided group addition law.

arXiv comment36 pages latex with epsf (two figures, not critical)

References in corpus (3)

• Quantum group gauge theory on quantum spaces
• Braided Momentum Structure of the q-Poincare Group
• Braided Geometry of the Conformal Algebra

Cited by in corpus (4)

• Quantum Groups and Noncommutative Geometry
• Conceptual Issues for Noncommutative Gravity on Algebras and Finite Sets
• Quantum gravity on polygons and $\mathbb{R}\times {\mathbb{Z}}_n$ FLRW model
• Bicrossproduct approach to the Connes-Moscovici Hopf algebra