Incredible connections
Monstrous moonshine
normed alternative algebras over R:
- R/C/H/O
- simple complex Lie algebras
- formally real Jordan algebras
More distantly:
- Bott Periodicity
- classification of finite simple groups
Basic idea:
- every basic symmetry
(with possible rare exceptions: the 6 weird sporadic groups,
not in the Happy family (20 sporadic simple groups subgroups of
Monster))
comes from the alternative algebras
- these come in 4 families: R (even/odd), C, H,
and exceptions come from the octonions
Exceptional items:
Octonions
E_8 lattice
triality
Leech lattice (24-dimensional; comes from E_8 and triality)
Monster group
binary Golay codes
Steiner system S(5,8,24)
(there are other sporadic/Golay/Steiner connections)