A meeting of the North British Functional Analysis Seminar will be held at the University of Glasgow from 2.30pm on Friday 1st November until noon on Saturday 2nd November 1996. Lectures will be held in the Department of Mathematics.
Abstract: For any locally compact abelian group $G$, one can consider the dual group $\hat G$ which is again a locally compact abelian group. Pontryagin's duality theorem states that the dual of $\hat G$ is canonically isomorphic with $G$. If $G$ is compact, then $\hat G$ is discrete. This duality is the basis of abstract harmonic analysis. \indent There have been several attemps to generalize this basic theorem of Pontryagin to the non-abelian case. Some of these extensions have been obtained within one category of objects, but in most cases, the theory is quite involved (e.g. Kac Algebras). \indent In this talk, we want to present a category of objects (the 'Algebraic Quantum Groups') that contain the discrete (quantum) groups and the compact (quantum) groups and which is self-dual. The objects are multiplier Hopf algebras (a natural extension of the notion of a Hopf algebra to the case of algebras without identity) with invariant functionals (left and right Haar measures).
All interested are welcome to attend.
The NBFAS Committee Meeting will be held in the Mathematics Department at 5.00pm on Friday 1st November.
For further information please contact Dr. G. Blower (Secretary),