A possible mathematics for the unification of quantum mechanics and general relativity A CP-violating kinematic structure AIP Conf. Proc. 566, 317 (2001); 10.1063/1.1378641
SU(2) quantum kinematics: Rotation-observable versus angular-momentum generalized commutation relationsThe quantum group and space theory is reformulated from the standard skewsymmetric basis to an arbitrary one. The N-dimensional quantum Cayley-Klein spaces are described in Cartesian basis and the quantum analogs of ͑N −1͒-dimensional constant curvature spaces are introduced. Part of the fourdimensional constant curvature spaces are interpreted as the noncommutative analogs of ͑1+3͒ space-time models. As a result the quantum ͑anti͒ de Sitter, Minkowski, Newton, Galilei, Carroll kinematics with the fundamental length and the fundamental time are suggested.
Possible contractions of quantum orthogonal groups which correspond to
different choices of primitive elements of Hopf algebra are considered and all
allowed contractions in Cayley--Klein scheme are obtained. Quantum deformations
of kinematical groups have been investigated and have shown that quantum analog
of (complex) Galilei group G(1,3) do not exist in our scheme.Comment: 10 pages, Latex. Report given at XXIII Int. Colloquium on Group
Theoretical Methods in Physics, July 31- August 5, 2000, Dubna (Russia
The similarity transformations of quantum orthogonal groups are developed and FRT theory is reformulated to the Cartesian basis. The quantum orthogonal Cayley-Klein groups are introduced as the algebra functions over an associative algebra with the nilpotent generators. The quantum orthogonal Cayley-Klein algebras are obtained as the dual objects to the corresponding quantum groups.
We define a class of orthosymplectic superalgebras osp(m; j|2n; ω) which may be obtained from osp(m|2n) by contractions and analytic continuations in a similar way as the orthogonal and the symplectic Cayley-Klein algebras are obtained from the corresponding classical ones. Contractions of osp(1|2) and osp(3|2) are regarded as an examples.
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