QUANTUM GROUPS, Q-OSCILLATORS, AND COVARIANT ALGEBRAS

The physical interpretation of the basic concepts of the theory of covariant groups - coproducts, representations and corepresentations, action and coaction - is discussed for the examples of the simplest q deformed objects (quantum groups and algebras, q oscillators, and comodule algebras). It is shown that the reduction of the covariant algebra of quantum second-rank tensors includes the algebras of the q oscillator and quantum sphere. A special case of covariant algebra corresponds to the braid group in a space with nontrivial topology.