What are...Borcherds-Kac-Moody algebras?

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 are...Borcherds-Kac-Moody algebras? Or: Still emerging from matrices.

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.
https://upload.wikimedia.org/wikipedi...
https://upload.wikimedia.org/wikipedi...

Main discussion.
https://link.springer.com/book/10.100...
https://darkwing.uoregon.edu/~klesh/t...
https://en.wikipedia.org/wiki/Kac%E2%...
https://ncatlab.org/nlab/show/Kac-Moo...
https://math.berkeley.edu/~barrett/re...
https://en.wikipedia.org/wiki/General...
https://en.wikipedia.org/wiki/Weyl_ch...
https://en.wikipedia.org/wiki/Monstro...
https://www.ams.org/notices/200209/wh...

Background material.
https://en.wikipedia.org/wiki/Weyl_ch...
https://en.wikipedia.org/wiki/Cartan_...
https://en.wikipedia.org/wiki/Lie_group
https://en.wikipedia.org/wiki/Lie_alg...
https://en.wikipedia.org/wiki/Affine_...
https://en.wikipedia.org/wiki/Macdona...
https://en.wikipedia.org/wiki/Root_sy...

Computer talk.
https://demonstrations.wolfram.com/Dy...
https://doc.sagemath.org/html/en/refe...
https://doc.sagemath.org/html/en/refe...
https://doc.sagemath.org/html/en/refe...
https://doc.sagemath.org/html/en/refe...
https://doc.sagemath.org/html/en/refe...
https://doc.sagemath.org/html/en/them...

Pictures used.
Picture from https://en.wikipedia.org/wiki/J-invar...
Picture from https://en.wikipedia.org/wiki/Monstro...
https://en.wikipedia.org/wiki/Moon#/m...
https://en.wikipedia.org/wiki/Fano_pl...
https://en.wikipedia.org/wiki/Hall%E2...
https://upload.wikimedia.org/wikipedi...
https://upload.wikimedia.org/wikipedi...
Picture from https://bookstore.ams.org/view?Produc...
Picture from https://www.ams.org/notices/200209/wh...

YouTube and co.
   • Why study Lie theory? | Lie groups, a...  
   • Lie groups and Lie algebras: The Lie ...  
   • WHCGP: Natalie Paquette, "Borcherds-K...  
   • Generalized Kac-Moody Superalgebras a...  

#algebra
#numbertheory
#mathematics