It is a classical result that semisimple complex Lie algebras are classified by their root systems. The definition of a root system requires that it is invariant by the orthogonal reflection associated with a root.

In 2023 Dimitrov and Fioresi introduced generalized root systems by weakening the axioms of a root system considerably. They provided a classification in the rank 2 case and observed that all examples are equivalent to quotients of classical root systems. In joint work with Cuntz this result was extended to the higher rank case.

In my talk I will recaII some classical results about root systems and discuss their quotients. I will then explain the main ideas of the proof of the classification of generalized root systems.

Referent: Prof. Dr. Bernhard M. Mühlherr, Universität Gießen

Der Vortrag findet um 17.15 Uhr im Raum 210 des Mathematik-Gebäudes 48 statt.

Studierende, Doktorandinnen und Doktoranden sowie Wissenschaftlerinnen und Wissenschaftler des Fachbereichs Mathematik der RPTU und des Fraunhofer ITWM sind herzlich zum Kolloquium eingeladen!

Bild: iStock