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 theq oscillator and quantum sphere. A special case of covariant algebra corresponds to the braid group in a space with nontrivial topology.