Vinberg lecture part 3. Kac-Moody algebras

This lecture is part of a series which gives an expanded version of the Vinberg lecture on "Vinberg's algorithm and Kac-Moody algebras". This video is part 3 and describes how to associate Lie algebras to some hyperbolic reflection groups.
The original version of the Vinberg lecture is here:
amathr.org/Bor...
For the other lectures see
• Vinberg lecture

[@sergey7375]

Thank you for such lucid explanations! Any chance on discussing applications of KM algebras in quantum field theory?

[@louiswhaley258]

Thank you for these lectures! Finally, I'm able to bridge the gap conceptually between why physicists are so keen on symmetry groups. I think it goes like this (correct me if I'm wrong)....as of the '60's physicists had the "bootstrap idea" that all of a zoo of particles and their interactions with one another could be fit into one description, guided in an essential way by symmetry and therefore, symmetry groups, which describe the dynamics without trying to do the impossible, like giving an exact description of what will happen to a black box of particles that interact with each other. Instead, a probabilistic description can be developed if the group symmetry of the contents of the box are obtained from the known ways they interact. It goes like this: [particles, fields, wavefunctions, operators, matrixes]-->[relationships between each]-->[symmetries respected by transformations among these]-->[Symmetry groups]. Then from abstract algebra came this: [abstract algebras]-->[generalized algebras like Kac-Moody]-->[Matrix representations, root systems, irreducible stuff]--> [Dynkin and related diagrams]-->[symmetry groups]. Now the whole picture is being worked out in exacting detail...hence particle physics meets cosmology! It's beautiful and I share in some small way the appreciation you must have. Keep going....

[@louiswhaley258]

I forgot to add a wish, that you say a little something about the physicist Tony Smith, who's web pages included many disjoint sets of topics, including his TOE called "Voudoo" Physics or something. I believe he passed away recently and his contributions of articles on his home page were like manna from heaven to us amateur physicists. He has been mentioned in the blogs of many others like the home page of one Peter Woit. Thanks.

[@JAYMOAP]

This is very good, amazing work

[@JAYMOAP]

Thank you