B5742 - ALGEBRE

Learning outcomes

Students will acquire basic knowledge on associative and Lie algebras and their representations.

Course contents

- Introduction to the theory of associative algebras: definitions, examples, semisimple algebras, tensor algebras and their significant quotients (symmetric, exterior, enveloping).

- Introduction to the theory of the representations of associative algebras: Schur's Lemma, Jordan-Holder Theorem, Krull-Schmidt Theorem, Artin-Wedderburn Theorem.

- Introduction to the theory of finite-dimensional Lie algebras and their representations: Engel Theorem, Lie Theorem, Weyl Theorem. Verma modules. Example: the representations of sl(n).

Readings/Bibliography

K. Erdmann, T. Holm, Algebras and Representation Theory, Springer Undergraduate Math Series

P. Etingof, Introduction to Representation Theory

J.P. Serre, Lie Algebras and Lie Groups, Lecture notes in mathematics

Teaching methods

Lectures at the blackboard

Assessment methods

Discussion on assigned exercises and oral exam.

 

Students with specific learning disorders (SLD) or temporary or permanent disabilities are advised to contact the relevant University office well in advance (https://site.unibo.it/studenti-con-disabilita-e-dsa/it). That office will propose any necessary accommodations to the students concerned; however, these proposals must be submitted to the instructor for approval at least 15 days in advance, so that their appropriateness can be assessed in relation to the course's learning objectives.

The use of AI for assessment purposes is prohibited. Any use constitutes a violation of academic integrity.

Teaching tools

Tutoring

Office hours

See the website of Nicoletta Cantarini

See the website of Luca Migliorini