QUANTUM GROUPS, Q-OSCILLATORS, AND COVARIANT ALGEBRAS

The physical interpretation of the basic concepts of the theory of cov ariant groups - coproducts, representations and corepresentations, act ion and coaction - is discussed for the examples of the simplest q def ormed objects (quantum groups and algebras, q oscillators, and comodul e algebras). It is shown that the reduction of the covariant algebra o f quantum second-rank tensors includes the algebras of the q oscillato r and quantum sphere. A special case of covariant algebra corresponds to the braid group in a space with nontrivial topology.