Anyonic Behavior of Quantum Group Fermionic and Bosonic Systems

The role of quantum groups and quantum Lie algebras [1] in physics has its origin in the theory of vertex models [2] and the quantum inverse scattering method [3]. From the mathematical point of view, two of the most important developments have been their understanding in terms of the theory of noncommutative Hopf algebras [4] and their relation to non-commutative geometry [5, 6, 7]. In recent years the study of quantum groups and quantum algebras has greatly diversified into several areas of theoretical physics. Based on quantum group ideas, a considerable amount of work was devoted towards a formulation of the so called q-deformed physical systems. These approaches are attempts to develop more general formulations of quantum mechanics [8] and field theory [9, 10]. The main motivation behind this type of projects resides Talk given at International Conference on Orbis Scientae 1997, January 23-26 Miami, Florida [email protected]