By Vladimir G Turaev
Within the final decade we have now witnessed the delivery of a interesting new mathematical concept. it is usually known as by way of algebraists the speculation of quantum teams and via topologists quantum topology. those phrases, notwithstanding, appear to be too restrictive and don't exhibit the breadth of this new area that's heavily with regards to the conception of von Neumann algebras, the idea of Hopf algebras, the conception of representations of semisimple Lie algebras, the topology of knots, and so on. the main surprising achievements during this thought are headquartered round quantum teams and invariants of knots and three-dimensional manifolds.
The complete thought has been, to a superb volume, encouraged by way of rules that arose in theoretical physics. one of the suitable components of physics are the speculation of precisely solvable types of statistical mechanics, the quantum inverse scattering approach, the quantum thought of angular momentum, 2-dimensional conformal box thought, and so forth. the improvement of this topic indicates once again that physics and arithmetic intercommunicate and effect one another to the revenue of either disciplines.