1 Quantum Symmetry

Often quantum symmetry is understood in terms of properties of symmetry groups, their representations and related algebras. Quantum groups also possess quantum symmetries which are distinct from those exhibited by classical Lie groups, groups of rotations and Poisson or Lorentz transformation groups. Extended quantum symmetries are also encountered for quantum groupoids, quantum categories, Hamilton algebroids, graded Lie super-algebras, Lie algebroids and quantum systems with topological order.