The n-Category Café

So, what’s the verdict? What is the Monster 2-group?

I went to Nora’s talk, but unfortunately I didn’t catch the definition.

I also asked David Roberts on Google+, who answered

The overarching aim is to categorify certain aspects of John McKay’s work.

The specific aim is to show that certain finite groups are the group of isomorphism classes of certain 2-groups, or for the case of skeletal 2-groups or strict 2-groups, the group of objects. One of her students did this for the platonic groups (certain groups embeddable in $Spin(3) ~ S^3$), and this involved $String(3)$.

One of the key techniques is to consider a categorification of the relationship between Lie groups, maximal tori and Weyl groups, so that one can relate the Lie side of things and the discrete side of things. Using the torus given by the Leech lattice she says she can push this programme up to $Co_0$ = Aut(Leech lattice).

Another point is that she (and collaborators) want to get the Monster 2-group as the autoequivalence 2-group of some reasonably natural object in a 2-category, and it looks like an Enhanced TFT (something like a stripped down CFT) will be such a thing. At any rate, something simpler than the Frenkel, Lepowsky, Meurman VOA (‘simpler’ in some sense). (looking around I find this which might interest you)

When I talked with her, I forgot to ask about the sporadics being ‘things which are accidentally groups’, I’ll bring it up again.

So it’s not there yet, but a clear programme to build towards it is well under way.