- Docente: Alessandro D'Andrea
- Credits: 6
- SSD: MATH-02/A
- Language: English
- Teaching Mode: In-person learning (entirely or partially)
- Campus: Bologna
- Corso: Second cycle degree programme (LM) in Mathematics (cod. 6730)
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from Sep 15, 2026 to Dec 16, 2026
Learning outcomes
At the end of the course, the student knows the fundamental notions of finite-dimensional Lie algebras and their representation theory. The student is able to handle the main tools of this theory that can be used to construct mathematical models.
Course contents
By the end of the course, students will understand the main structural results for finite-dimensional Lie algebras and the foundations of their representation theory. They will be able to work with the standard methods used to study semisimple Lie algebras and their finite-dimensional representations.
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Finite-dimensional Lie algebras over an algebraically closed field of characteristic zero. Solvable and nilpotent Lie algebras. Semisimple Lie algebras, root decompositions and classification. Finite-dimensional representations of semisimple Lie algebras, highest weights and classification of irreducible representations.
Readings/Bibliography
J. E. Humphreys, Introduction to Lie Algebras and Representation Theory, Springer.
V. Kac, MIT lecture notes on Lie algebras.
K. McGerty, online lecture notes on Lie algebras.
Teaching methods
Chalk and blackboard.
Problem sets will be circulated at irregular intervals.
Assessment methods
The examination is oral. Students may also be required to submit selected solutions from the problem sets.
Teaching tools
Course materials will be made available on Virtuale.
Office hours
See the website of Alessandro D'Andrea