Module page
Istituzioni di Algebra Superiore
| academic year: | 2013/2014 |
| instructor: | Paolo Papi |
| degree course: | Mathematics (magistrale) |
| type of training activity: | caratterizzante |
| credits: | 9 (72 class hours) |
| scientific sector: | MAT/02 Algebra |
| teaching language: | italiano |
| period: | I sem (30/09/2013 - 17/01/2014) |
Lecture meeting time and location
Presence: highly recommended
Module aims: The course gives a thorough introduction to the theory semisimple Lie algebras and their finite dimensional representations.
Module subject: Basic concepts, representation of solvable and nilpotent Lie algebras, Cartan subalgebras, Cartan decomposition, root system and Weyl group, Cartan matrices and Dynkin diagrams, existence and uniqueness theorems, simple Lie algebras, enveloping algebras, irreducible modules, character formulas, fundamental representations
Suggested reading: J.E. Humphreys, Introduction to Lie algebras and their representations, Graduate texts in Mathematics, Springer Verlag. R. Carter, Lie Algebras of Finite and Affine Type (Cambridge Studies in Advanced Mathematics). Karin Erdmann and Mark J. Wildon, Introduction to Lie algebras, Springer Verlag.
Type of course: standard
Useful links:
- Test del 4-11
- Testo della prima prova in itinere
- Soluzioni (schematica) della prima prova in itinere
- Esercizi di Natale
- testo e traccia delle soluzioni della seconda prova in itinere
- Esercizi da consegnare per la prova del 23-1
- Esercizi da consegnare per la prova del 13-2
- Esercizi da consegnare per la prova del 24-4
- prova scritta gennaio
- prova scritta febbraio
- prova scritta 1 luglio
- Esercizi da consegnare per l'esame del 22-7
- prova scritta del 29-9
- esercizi da consegnare per la prova del 29-9
- prova appello straordinario 10-11
Knowledge and understanding: A the end of the course the student will be familiar with the classification of such algebra of their finite dimensional irreducible modules and with formulas expressing their characters.
Skills and attributes: At the end of the course students should be able to read research papers dealing with the theory of semisimple Lie algebras.
Personal study: the percentage of personal study required by this course is the 65% of the total.