What are...Borcherds-Kac-Moody algebras?
HTML-код
- Опубликовано: 3 окт 2024
- 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.
www.dtubbenhaue...
TeX files for the presentation.
github.com/dtu...
Thumbnail.
upload.wikimed...
upload.wikimed...
Main discussion.
link.springer....
darkwing.uoreg...
en.wikipedia.o...
ncatlab.org/nl...
math.berkeley....
en.wikipedia.o...
en.wikipedia.o...
en.wikipedia.o...
www.ams.org/no...
Background material.
en.wikipedia.o...
en.wikipedia.o...
en.wikipedia.o...
en.wikipedia.o...
en.wikipedia.o...
en.wikipedia.o...
en.wikipedia.o...
Computer talk.
demonstrations...
doc.sagemath.o...
doc.sagemath.o...
doc.sagemath.o...
doc.sagemath.o...
doc.sagemath.o...
doc.sagemath.o...
Pictures used.
Picture from en.wikipedia.o...
Picture from en.wikipedia.o...
en.wikipedia.o...
en.wikipedia.o...
en.wikipedia.o...
upload.wikimed...
upload.wikimed...
Picture from bookstore.ams....
Picture from www.ams.org/no...
RUclips and co.
• Why study Lie theory? ...
• Lie groups and Lie alg...
• WHCGP: Natalie Paquett...
• Generalized Kac-Moody ...
#algebra
#numbertheory
#mathematics
![NOSFERATU - Official Trailer [HD] - Only In Theaters December 25](http://i.ytimg.com/vi/nulvWqYUM8k/mqdefault.jpg)
Very nice. Richard has new lecture series up also on this.
Yes, I wanted to check it out.
What about a video of your LFTs, least favorite theorems ?
I like all theorems 😅
@@VisualMath But do you like them all equally? 🤔
@@mrl9418 I only have indiscriminate love to offer ☺
Maybe Monstrous moonshine can be explained by taking the McKay quiver for the finite group G that also happens to be a simple group as well in this case. The quiver of its Kac-Moody algebra could also be considered instead.
The quiver is a directed graph with additional structure and a simplicial set A. Note from category theory directed graphs with additional structure are considered categories. Would need more justification but, assume that A is the simplicial set of the nerve of N(C) of a small category C.
The small category C in the case of the Monster group is a subcategory of elliptic curves classified by the j-invariant. The geometric realization of the simplicial set A is its classifying space BC. Classifying spaces describe the topology of the geometric moduli space.
That is a nice one!
I still like Borcherds construction more as it immediately gives the monster as well.
@@VisualMath Same here 👍
What is interesting is the kac moody and Virasoro algebras consistent in condensed matter physics (quantum hall systems but it's lower dimension) in my opinion the higher dimensional algebras not physically consistent but rather representation of degrees of freedom on a disk