In the case where $C$ is the Golay code, $Λ_C$ is the Leech lattice and the induced triality is the extra symmetry necessary to generate the Monster group from (an extension of) Conway's group. Thus it is demonstrated that triality is a generic symmetry.

9 years ago

Kea,

ReplyDeleteChapel Hill seemed very much a magical place where we spent a long time in the quad talking to students. I was not easy to try to classify melody with twelve dimensions. String theory began to arise then. I assume Ms. Dolan does use the term "affine" in the sense I understand it from contexts.

This paper is right on and ahead of its time. But there is more to it than the superstructures. 24 , 48 could be- Conway? well, there is more to number than the surreal. Even and odd groups? That is a start. Guess it all comes back in the lower space of 4D with 384 hypercube rotations. 8n involved here as I too see.

I cannot say I grasp how the monster group arises (the math) but I know 240 is the 8 natural hypersphere close packing- and that number 24 is unique in the sums and recently in fractal patterns. Triality is not only generic in particle terms it is generational.

The PeSla

Oh, thanks for the inspiration to have me look a little at the physics and math disconnect.

You are most welcome, The Pe Sla. Mitchell has kindly sent me the paper, so that I can now read it myself.

ReplyDeleteThat's Professor Dolan, by the way.

ReplyDeleteSorry, I was sort of ignoring the other names after her on that paper on principle.

ReplyDeletePe Sla

Yes, The Pe Sla, that is a useful exercise. That is why I intend only writing solo author papers from now on.

ReplyDelete