Departamento de Álgebra

Universidad de Granada

Curso

Non Commutative Algebraic Geometry by Examples

por

Lieven Le Bruyn, Amberes

Fechas: del 4 al 8 de abril de 2005

Horario: 11h. - 13h., diario

Lugar: Aula de Conferencias (M1) de la Facultad de Ciencias, Fuentenueva s/n, Granada.

Abstract

In this course we will give an introduction to non-commutative algebraic geometry as proposed by D. Quillen and M. Kontsevich and which is based on noncommutative (formally) smooth algebras. We will study the noncommutative varieties associated to interesting arithmetical groups such as SL₂(Z) and GL₂(Z) (which will turn out to be noncommutative manifolds) and the third braid group B₃ (which will be singular). We will explain how noncommutative geometry can help in studying representations of these groups and (if time allows) we will construct noncommutative compactifications of them. All necessary concepts will be recalled but some familiarity with finite groups and their representations and/or matrix algebras may be useful. Notes will be provided.