Seidon Alsaody: Exceptional Groups and Exceptional Algebras

  • Datum: –10.15
  • Plats: Ångströmlaboratoriet 4101
  • Arrangör: Matematiska institutionen
  • Kontaktperson: Inger Sigstam
  • Seminarium

The Cartan-Killing classification of simple complex Lie algebras is a principal result of the past century. With its four infinite families and five exceptions, it provides a classification both on the level of Lie groups and of algebraic groups. For the latter, this can be extended to a solid theory of group schemes over arbitrary commutative rings. This is useful in geometry and number theory, and achieved through the algebraic geometry developed by the school of Grothendieck.

Exceptional groups are related to algebras and other objects that are themselves in some sense exceptional, such as composition algebras, triality, and exceptional Jordan algebras. I will report on recent work, studying these groups and objects over rings from a geometric point of view, using homogeneous spaces (torsors) under exceptional groups. As it turns out, this not only provides a new framework to familiar constructions, but unveils irregularities and new structures that were not expected from the objects' behaviour in the classical setting.