Quantum Groups, $q$-Oscillators and Covariant Algebras

Details Quantum Groups, $q$-Oscillators and Covariant Algebras Quantum Groups, $q$-Oscillators and Covariant Algebras

1992-09-17

arxiv.org/abs/hep-th/9209060v1

Theor.Math.Phys. 94 (1993) 137-141; Teor.Mat.Fiz. 94N2 (1993) 193-199

Physics

High Energy Physics

High Energy Physics - Theory

11 pages. (Figures are not included.) Dedicated to the memory of M. C. Polivanov

Scientific paper

10.1007/BF01019325

The physical interpretation of the main notions of the quantum group theory (coproduct, representations and corepresentations, action and coaction) is discussed using the simplest examples of $q$-deformed objects (quantum group $F_q(GL(2))$, quantum algebra $sl_q(2)$, $q$-oscillator and $F_q$-covariant algebra.) Appropriate reductions of the covariant algebra of second rank $q$-tensors give rise to the algebras of the $q$-oscillator and the $q$-sphere. A special covariant algebra related to the reflection equation corresponds to the braid group in a space with nontrivial topology.

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