Cayley-Klein Lie Algebras and their Quantum Universal Enveloping Algebras

Details Cayley-Klein Lie Algebras and their Quantum Universal Enveloping Algebras Cayley-Klein Lie Algebras and their Quantum Universal Enveloping Algebras

1994-02-20

arxiv.org/abs/hep-th/9402116v1

Physics

High Energy Physics

High Energy Physics - Theory

7 pages, AMS-TEX file, UVA/93-102

Scientific paper

The N-dimensional Cayley-Klein scheme allows the simultaneous description of $3^N$ geometries (symmetric orthogonal homogeneous spaces) by means of a set of Lie algebras depending on $N$ real parameters. We present here a quantum deformation of the Lie algebras generating the groups of motion of the two and three dimensional Cayley-Klein geometries. This deformation (Hopf algebra structure) is presented in a compact form by using a formalism developed for the case of (quasi) free Lie algebras. Their quasitriangularity (i.e., the most usual way to study the associativity of their dual objects, the quantum groups) is also discussed.

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