Noncommutative space-time models

Abstract

The FRT quantum Euclidean spaces $O_q^N$ are formulated in terms of Cartesian generators. The quantum analogs of N-dimensional Cayley-Klein spaces are obtained by contractions and analytical continuations. Noncommutative constant curvature spaces are introduced as a spheres in the quantum Cayley-Klein spaces. For N=5 part of them are interpreted as the noncommutative analogs of (1+3) space-time models. As a result the quantum (anti) de Sitter, Newton, Galilei kinematics with the fundamental length and the fundamental time are suggested.

8 pages; talk given at XIV International Colloquium of Integrable Systems, Prague, June 16-18, 2005

References in corpus (1)

• Field theory on kappa-spacetime

Cited by in corpus (2)

• Erlangen Program at Large-2.5: Induced Representations and Hypercomplex Numbers
• Erlangen Program at Large-1: Geometry of Invariants