UCL - Galois theory and groups representtions

[MAT2120]

[45h + 15h] 5 credits

This course is taught in the 2d semester.

Teacher(s): Pierre-Emmanuel Caprace, Jean-Pierre Tignol

Language: French

Level: Second

Aims
Main themes
Other information (prerequisite, evaluation (assessment methods), course materials recommended readings, ...)

Aims

After this course, students should be able to use the methods of abstract algebra to analyse situations with a high degree of symmetry and those where the rationality domain plays an important role, such as questions of solvability by radicals, and ruler and compass constructions. A special emphasis will be laid on techniques which use the representation of symmetry groups as groups of vector space transformations.

Main themes

Galois theory: field extensions and their automorphisms; translation of field extensions properties in terms of the associated groups and applications to some classical problems (solvability by radicals, ruler and compass constructions).Group representations: character of a linear representation; group algebras and induced representations.

Other information (prerequisite, evaluation (assessment methods), course materials recommended readings, ...)

Precursorycourses A first course in linear algebra

Support J. Rotman : Galois theory (2d edition), Springer 1998J-P. Serre : Représentations linéaires des groupes finis, Hermann 1971