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arXiv · hep-th/9209060

Quantum Groups, $q$-Oscillators and Covariant Algebras

P. P. Kulish
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Abstract

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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P. P. Kulish. 1992-09-17. Quantum Groups, $q$-Oscillators and Covariant Algebras. https://doi.org/10.1007/bf01019325

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