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

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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.

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TeX files for the presentation.

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Computer talk.

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#algebra
#numbertheory
#mathematics
  1. VisualMath
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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.

Jaylooker
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What about a video of your LFTs, least favorite theorems ?

mrl