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Universität Augsburg
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Universität Augsburg
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Prof. Em. Dr. Jost-Hinrich Eschenburg
Universität Augsburg
spricht am
Montag, 6. Februar 2023
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16 Uhr s.t.
im
Raum L1/2004 bzw. ZOOM (hybride Veranstaltung)
über das Thema:
| Abstract: |
| A finite dimensional real algebra A with unit is called normed if |ab| = |a||b| for all a,b in A for some (necessarily euclidean) norm on A. Essentially there is only one normed algebra, the octonions O, and the real, complex, and quaternionic numbers are the normed subalgebras. The octonions are the source of exceptional symmetric spaces. As explained in an earlier talk, beneath the exceptional Lie groups there are 12 exceptional compact irreducible symmetric spaces: the four Rosenfeld planes (dimensions 16, 32, 64, 128), certain spaces of subspaces of Rosenfeld planes, and the space X of quaternionic subalgebras of O. This last space will be will be the subject of the present talk: It is the 8-dimensional quaternionic symmetric space Aut(O)/SO(4). We will derive the structure of O from the definition of normed algebras and relate it to the root diagrams (Dynkin diagrams) of Aut(O) and X which are both of type G2 (star of David). |
| Hierzu ergeht herzliche Einladung. |
| Prof. Dr. Bernhard Hanke |
Kaffee, Tee und Gebäck eine halbe Stunde vor Vortragsbeginn im Raum 2006 (L1).