PlanetPhysics/Quantum Transformation Groupoid

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Quantum transformation groupoidEdit

This is a quantum analog construction of the classical transformation group construction via the action of a group on a state (or phase) space.

Let us a consider a locally compact quantum group (L-CQG),   and also let   be a locally compact space underlying   . If   and   are von Neumann algebras and   is a (von Neumann) locally compact group, then one can define the following representations of   on a Hilbert space  :

    with   being the left action of   on  .

A quantum transformation groupoid   is defined by the   left action of   on   which has the above representations of  .