Lecture: Geometry of Octonions - Details

General information

Course name	Lecture: Geometry of Octonions
Semester	SS 2018
Current number of participants	3
Home institute	Differentialgeometrie
Courses type	Lecture in category Teaching
First date	Wednesday, 11.04.2018 14:00 - 15:30
Type/Form	Vorlesung
Veranstaltung findet online statt / hat Remote-Bestandteile	Yes
Hauptunterrichtssprache	englisch

Lecturers

• Prof.Dr. Jost-Hinrich Eschenburg

Rooms and times

No room preference

Wednesday: 14:00 - 15:30, weekly

Fields of study

• Mathematisch-Naturwissenschaftlich-Technische Fakultät > Institut für Mathematik > Lehramt am Gymnasium (Mathematik)
• Mathematisch-Naturwissenschaftlich-Technische Fakultät > Institut für Mathematik > Bachelor Mathematik
• Mathematisch-Naturwissenschaftlich-Technische Fakultät > Institut für Mathematik > Master Mathematik

Comment/Description

The simple classical compact groups SO(n), SU(n), Sp(n) are related
to the division algebras R,C,H (reals, complex numbers, quaternions).
The exceptional groups G_2, F_4, E_6, E_7, E_8 are somehow related
to the remaining normed division algebra, the octonions O, but
the relation is not quite easy to understand, except for G_2 = Aut(O).

We will start with Hurwitz' theorem that R,C,H,O are all possible
normed division algebras over the reals (including construction).
Then we will turn to the octonionic projective plane and its
connection to F_4 and E_6. I might tell what I know about
the relation to E_7 and E_8. If there is interest, I could
also explain the relation of the octonions to real Bott
periodicity.