4D Quantum Affine Algebras and Space--Time q-Symmetries

Details 4D Quantum Affine Algebras and Space--Time q-Symmetries 4D Quantum Affine Algebras and Space--Time q-Symmetries

1993-10-21

arxiv.org/abs/hep-th/9310140v1

J.Math.Phys. 35 (1994) 4928-4940

Physics

High Energy Physics

High Energy Physics - Theory

13 pages, AMS-TEX file

Scientific paper

10.1063/1.530823

A global model of $q$-deformation for the quasi--orthogonal Lie algebras generating the groups of motions of the four--dimensional affine Cayley--Klein geometries is obtained starting from the three dimensional deformations. It is shown how the main algebraic classical properties of the CK systems can be implemented in the quantum case. Quantum deformed versions of either the space--time or space symmetry algebras (Poincar\'e (3+1), Galilei (3+1), 4D Euclidean as well as others) appear in this context as particular cases and several $q$-deformations for them are directly obtained.

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