Seminar on Lie Algebras and Representation Theory

The seminar will take place on Tuesday, 16-18 in room WSC-N-U-4.04.

Everyone is welcome to attend the seminars, even without registering or giving a talk.

Abstract: Lie algebras arise naturally in the study of symmetries of mathematical objects and play a fundamental role in algebra and geometry. Roughly speaking, they capture the ``infinitesimal behavior'' of group actions, allowing us to study symmetries through the more linear framework of algebra. This perspective brings powerful tools from linear algebra and combinatorics into play and leads to the elegant classification of semisimple Lie algebras, which we will develop throughout this seminar. To any algebraic (or Lie) group $G$, we can functorially associate a finite-dimensional Lie algebra $\mathfrak{g}$. In the final lectures, we will explore the relationship between groups and their associated Lie algebras. We will conclude by emphasizing how the representation category $\operatorname{Rep}(G)$ can be understood through the corresponding category $\operatorname{Rep}(\mathfrak{g})$.

Prerequisites: A first course in the representation theory of finite groups is recommended but not necessary. Towards the end, we will assume a bit of familiarity with affine algebraic varieties. In particular, we will use the tangent bundle, which will be recalled in one of the last talks.

Program: seminar schedule.

If you'd like to enrol, please register on the moodle page (password: "semisimple").