Quantum Groups, $q$-Oscillators and Covariant Algebras
High Energy Physics - Theory
2009-10-22 v1 Quantum Algebra
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 -deformed objects (quantum group , quantum algebra , -oscillator and -covariant algebra.) Appropriate reductions of the covariant algebra of second rank -tensors give rise to the algebras of the -oscillator and the -sphere. A special covariant algebra related to the reflection equation corresponds to the braid group in a space with nontrivial topology.
Cite
@article{arxiv.hep-th/9209060,
title = {Quantum Groups, $q$-Oscillators and Covariant Algebras},
author = {P. P. Kulish},
journal= {arXiv preprint arXiv:hep-th/9209060},
year = {2009}
}
Comments
11 pages. (Figures are not included.) Dedicated to the memory of M. C. Polivanov