Borcherds’ monster papers

Yesterday morning I thought that I could use some discussions I had a week before with Markus Reineke to begin to make sense of one sentence in Kontsevich’ Arbeitstagung talk Non-commutative smooth spaces :

It seems plausible that Borcherds’ infinite rank algebras with Monstrous symmetry can be realized inside Hall-Ringel algebras for some small smooth noncommutative spaces

However, as I’m running on a 68K RAM-memory, I didn’t recall the fine details of all connections between the monster, moonshine, vertex algebras and the like. Fortunately, there is the vast amount of knowledge buried in the arXiv and a quick search on Borcherds gave me a list of 17 papers. Among these there are some delightful short (3 to 8 pages) expository papers that gave me a quick recap on things I once must have read but forgot. Moreover, Richard Borcherds has the gift of writing at the same time readable and informative papers. If you want to get to the essence of things in 15 minutes I can recommend What is a vertex algebra? (“The answer to the question in the title is that a vertex algebra is really a sort of commutative ring.”), What is moonshine? (“At the time he discovered these relations, several people thought it so unlikely that there could be a relation between the monster and the elliptic modular function that they politely told McKay that he was talking nonsense.”) and What is the monster? (“3. It is the automorphism group of the monster vertex algebra. (This is probably the best answer.)”). Borcherds maintains also his homepage on which I found a few more (longer) expository papers : Problems in moonshine and Automorphic forms and Lie algebras. After these preliminaries it was time for the real goodies such as The fake monster formal group, Quantum vertex algebras and the like.
After a day of enjoyable reading I think I’m again ‘a point’ wrt. vertex algebras. Unfortunately, I completely forgot what all this could have to do with Kontsevich’ remark…