- Docente: Nicoletta Cantarini
- Credits: 6
- SSD: MAT/02
- Language: Italian
- Moduli: Nicoletta Cantarini (Modulo 1) Luca Migliorini (Modulo 2)
- Teaching Mode: Traditional lectures (Modulo 1) Traditional lectures (Modulo 2)
- Campus: Bologna
- Corso: First cycle degree programme (L) in Mathematics (cod. 8010)
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from Feb 19, 2025 to May 30, 2025
Learning outcomes
Very roughly speaking, representation theory studies symmetry in linear spaces. It is a beautiful mathematical subject which has many applications, ranging from number theory and combinatorics to geometry, probability theory, quantum mechanics, and quantum field theory.
The goal of this course is to give an introduction to representation theory, presenting it as a unified subject which studies representations of associative algebras and treating the representation theories of groups, Lie algebras, and quivers as special cases.
Course contents
Basic notions of representation theory: algebras, irreducible representations, tensor product of representations, dual representations, semisimple representations
General results of representation theory: The density theorem, Representations of direct sums of matrix algebras, Filtrations, Finite dimensional algebras, Characters of representations, The Jordan-Holder theorem. The Krull-Schmidt theorem
Representations of finite groups: Maschke’s theorem. Characters.Frobenius determinant
Hints on Quiver representations
Readings/Bibliography
P. Etingof. Introduction to representation theory
https://math.mit.edu/~etingof/repb.pdf
Teaching methods
Lessons at the blackboard, discussion sessions
Assessment methods
Written and oral exam. Exercises sheets will be given to students and corrected in class
Teaching tools
Blackboard
Office hours
See the website of Nicoletta Cantarini
See the website of Luca Migliorini
SDGs

This teaching activity contributes to the achievement of the Sustainable Development Goals of the UN 2030 Agenda.