Locally compact quantum group

From Wikipedia, the free encyclopedia

You have new messages (last change).

The introduction to this article provides insufficient context for those unfamiliar with the subject matter.
Please help Wikipedia by improving the introduction according to the guidelines laid out at Wikipedia:Guide to layout. You can discuss the issue on the talk page.

The locally compact (l.c.) quantum group is a relatively new C*-algebraic formalism for quantum groups, generalizing the Kac algebra, compact quantum group and Hopf algebra approaches. Earlier attempts of a unifying definition of quantum groups using e.g multiplicative unitaries have had some success, but have also ran into several technical problems.

One of the main features distinguishing it from other approaches is the axiomatic existence of an invariant weight, giving a noncommutative analogue of the Haar measure.

The category of l.c. quantum groups allow for a dual construction, generalizing the Pontryagin duality of abelian groups.

The theory has an equivalent formulation in terms of von Neumann algebras.

Retrieved from "http://en.wikipedia.org../../../l/o/c/Locally_compact_quantum_group.html"