The Monster

December 13, 2009

For those who had a craving for some group theory images on this Sunday afternoon, fear not, I give thee E8, otherwise known as the monster.

For the more matematically inclined, the above image can be summarized by its Dynkin Diagram (the colors have no meaning):

E8 is a manifold of 248 dimensions, and its name comes from the fact that it has a rank of 8, the dimension of its root system is 8 (a 2-d projection of the root system is shown above, but is more succinctly described by the Dynkin diagram, which has 8 nodes to represent the 8 root vectors.)

But who cares about the math. The picture is pretty to look out.

Another fun group is the "Monster," which is an extremely large (but finite) simple group (simple meaning that it has no normal subgroups). It has dimension 808017424794512875886459904961710757005754368000000000, which is how it gets the name "monster." It is the largest of the so called "sporadic groups," which are the black sheep of attempts to neatly classify finite simple groups (simple groups are like the prime numbers of finite groups).

Here's where the monster stands in relation to the other sporadic groups: