2004/10/08 by N. A. Gromov, Gromov, N. A., V. V. Kuratov +1
Mathematics · Physics and Astronomy · #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Quantum Algebra (math.QA) #hep-th #math.QA
paper · pdf · doi:10.48550/arxiv.hep-th/0410086
Talk given at the Int. conference "Non-Commutative Geometry and Representation Theory in Mathematical Physics", 5-10 July, 2004, Karlstad, Sweden and at XI Int. conference "Symmetry Metods in Physics", 21-24 June, 2004, Prague, Czech Republic, 24 pages, 1 figure
The FRT quantum group and space theory is reformulated from the standard mathematical basis to an arbitrary one. The N-dimensional quantum vector Cayley-Klein spaces are described in Cartesian basis and the quantum analogs of (N-1)-dimensional constant curvature spaces are introduced. Part of the 4-dimensional constant curvature spaces are interpreted as the non-commutative analogs of (1+3) kinematics. A different unifications of Cayley-Klein and Hopf structures in a kinematics are described with the help of permutations. All permutations which lead to the physically nonequivalent kinematics are found and the corresponding non-commutative (1+3) kinematics are investigated. As a result the quantum (anti) de Sitter, Minkowski, Newton, Galilei kinematics with the fundamental length, the fundamental mass and the fundamental velocity are obtained.