Galois theory and groups representtions [ LMAT2120 ]
5.0 crédits ECTS
45.0 h + 15.0 h
2q
| Teacher(s) |
Caprace Pierre-Emmanuel ;
Tignol Jean-Pierre ;
|
| Language |
French
|
Place
of the course |
Louvain-la-Neuve
|
| 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.
|
| 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.
|
| Other information |
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
|
Cycle et année
d'étude |
> Master [60] in Mathematics
> Master [120] in Mathematics
|
Faculty or entity
in charge |
> MATH
|
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