ALGANT student seminar – Representation Theory
Date and time: Wednesday, March 21st, at 13:30
Room: Aula Chisini
Dott. ELIA CHINELLATO
Title: Roots systems
Abstract: The goal of this talk is to give a brief introduction to roots systems in an euclidean space, explaining some fundamental concepts, such as reflections in an euclidean space, the axioms for roots systems and the Weyl group. Examples will be given in euclidean spaces of dimension 1 and 2. The final part is dedicated to the definition and the construction of a base of a roots system.
Dott. CHIARA DAMIOLINI
Title: Projective representations
Abstract: The lecture will regard some applications of projective representations of finite groups. The main result will be the Schur’s theorem concerning central extensions of finite groups with projective lifting property, which is a very useful instrument to deduce information about the group. If there is more time we will see, using character triples, other results about characters induced by normal subgroups.
Dott. FRANCESCO MONOPOLI
Title: Levi’s and Ado’s theorems
Abstract: In this seminar I will prove the two theorems mentioned in the title. Levi’s theorem states that every Lie algebra can be written as the direct sum of its radical and a semisimple subalgebra, while Ado’s theorem says that every Lie algebra has a finite-dimensional faithful representation.
Dott. GIANPIETRO COLATO
title: Groups in categories
abstract: in the first part of the seminar we introduce the basic categorical language needed to define Lie groups and Lie algebras categories. In the second part we describe some results of the theory of smooth manifolds in terms of functors, natural transformations and universal constructions, focusing in particular on the Lie functor, which associates a Lie group to its Lie algebra of smooth left-invariant vector fields.
Anyone interested is invited.