Abstract
The N-dimensional Cayley-Klein scheme allows a simultaneous description of 3N 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 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 usual way to study the associativity of their dual objects, the quantum groups) is also discussed.
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© 1994 Springer Science+Business Media Dordrecht
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Ballesteros, A., Herranz, F.J., Del Olmo, M.A., Santander, M. (1994). Cayley-Klein Lie Algebras and Their Quantum Universal Enveloping Algebras. In: González, S. (eds) Non-Associative Algebra and Its Applications. Mathematics and Its Applications, vol 303. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-0990-1_4
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DOI: https://doi.org/10.1007/978-94-011-0990-1_4
Publisher Name: Springer, Dordrecht
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