Announcements

On October 2nd and 3rd the XXIst Meeting on representation theory of algebra will take place at the Universities of Sherbrooke and Bishop's.

What is the representation theory of algebras?

The idea to represent a complex mathematical object by a simpler one is as old as mathematics itself. The theory as such goes back to 1835, when W. R. Hamilton had the idea to represent complex numbers as pairs of real numbers.

In 1929, Emmy Noether has introduced the point of view which is generally accepted nowadays: to represent a ring A by means of the endomorphism ring End(G) of an abelian group G, which is often a ring Mn(K) of full nxn matrices over a field K.

This gave a unified setup allowing to consider several problems, such as the theory of quadratic forms as well as many problems of resolution of differential equations.

Since the ninety seventies, the representation theory of algebras has developed very fast. It is now one of the most active areas of algebras, interacting with, for instance, algebraic geometry, the theory of Lie algebras which appear also in physics, finite groups, quantum groups and also algebraic topology.