What is...Freudenthal’s magic square?
Goal.
I would like to tell you a bit about my favorite theorems, ideas or concepts in mathematics and why I like them so much.
This time.
What is...Freudenthal’s magic square? Or: Exceptional!
Disclaimer.
Nobody is perfect, and I might have said something silly. If there is any doubt, then please check the references.
Slides.
http://www.dtubbenhauer.com/youtube.html
TeX files for the presentation.
https://github.com/dtubbenhauer/My-Te...
Thumbnail.
Picture from https://en.wikipedia.org/wiki/Freuden...
Main discussion.
https://www.taylorfrancis.com/books/m...
https://link.springer.com/book/10.100...
https://www.ams.org/journals/bull/200...
https://en.wikipedia.org/wiki/Octonion
https://en.wikipedia.org/wiki/Octonio...
https://en.wikipedia.org/wiki/Hurwitz...)
https://en.wikipedia.org/wiki/Cayley%...
https://en.wikipedia.org/wiki/Composi...
https://en.wikipedia.org/wiki/Freuden...
https://golem.ph.utexas.edu/category/...
Background material.
https://en.wikipedia.org/wiki/Number#...
https://en.wikipedia.org/wiki/Real_nu...
https://en.wikipedia.org/wiki/Complex...
https://en.wikipedia.org/wiki/Quaternion
https://en.wikipedia.org/wiki/Quatern...
https://en.wikipedia.org/wiki/Sedenion
https://en.wikipedia.org/wiki/Hyperco...
https://en.wikipedia.org/wiki/Quadrat...
https://en.wikipedia.org/wiki/Associa...
https://en.wikipedia.org/wiki/Commuta...
https://en.wikipedia.org/wiki/Multipl...
Computer talk.
https://magma.maths.usyd.edu.au/magma...
https://doc.sagemath.org/html/en/refe...
https://mathematica.stackexchange.com...
Pictures used.
Picture from • What are...Kac-Moody algebras?
https://en.wikipedia.org/wiki/File:Fi...
Picture from https://en.wikipedia.org/wiki/Freuden...
Another picture from https://en.wikipedia.org/wiki/Freuden...
https://en.wikipedia.org/wiki/Fano_pl...
YouTube and co.
• JOHN BAEZ | SPLIT OCTONIONS and the ROLLIN...
• Video
• This Week's Finds 9: quaternions and octon...
#algebra
#representationtheory
#mathematics