Higher Algebra
- Professors:
- Cornalba Maurizio
- Year:
- 2017/2018
- Course code:
- 500687
- ECTS:
- 6
- SSD:
- MAT/02
- DM:
- 270/04
- Lessons:
- 48
- Period:
- I semester
- Language:
- Italian
Objectives
The aim of the course is to provide an introduction to the theory of Lie algebras.
Teaching methods
Lectures
Examination
Oral examination.
Prerequisites
I contenuti dei corsi di Algebra 1, Algebra 2, Algebra lineare e Geometria 1.
Syllabus
Lie algebras:
Semisimple endomorphisms; Jordan-Chevalley decomposition. Lie algebras and Lie groups. Ideals and subalgebras. Solvable and nilpotent Lie algebras. The theorems of Lie and Engel. Cartan subalgebras. Linear representations of Lie groups and algebras. Representations of sl(2,C). Semisimple Lie algebras. Semisimplicity criteria. Root systems and their classification. Classical Lie algebras. Exceptional Lie algebras. Finite-dimensional representations of semisimple Lie algebras.
Semisimple endomorphisms; Jordan-Chevalley decomposition. Lie algebras and Lie groups. Ideals and subalgebras. Solvable and nilpotent Lie algebras. The theorems of Lie and Engel. Cartan subalgebras. Linear representations of Lie groups and algebras. Representations of sl(2,C). Semisimple Lie algebras. Semisimplicity criteria. Root systems and their classification. Classical Lie algebras. Exceptional Lie algebras. Finite-dimensional representations of semisimple Lie algebras.
Bibliography
K. Erdmann, M.J. Wildon, Introduction to Lie Algebras, Springer 2006
J. Humphreys, Introduction to Lie Algebras and Representation Theory, Springer 1972
J.P. Serre, Algebres de Lie semi-simples complexes, Benjamin 1966
A. Kirillov, Introduction to Lie Groups and Lie Algebras, https://www.math.stonybrook.edu/~kirillov/mat552/liegroups.pdf
J. Bernstein, Lectures on Lie Algebras, http://www.math.tau.ac.il/~bernstei/Publication_list/publication_texts/bernsteinLieNotes_book.pdf
J. Humphreys, Introduction to Lie Algebras and Representation Theory, Springer 1972
J.P. Serre, Algebres de Lie semi-simples complexes, Benjamin 1966
A. Kirillov, Introduction to Lie Groups and Lie Algebras, https://www.math.stonybrook.edu/~kirillov/mat552/liegroups.pdf
J. Bernstein, Lectures on Lie Algebras, http://www.math.tau.ac.il/~bernstei/Publication_list/publication_texts/bernsteinLieNotes_book.pdf
Dipartimento di Matematica ''F. Casorati''
Università degli Studi di Pavia -
Via Ferrata, 5 - 27100 Pavia
Tel +39.0382.985600 - Fax +39.0382.985602