This is the *Dynkin Diagram* of E_{8}.
See what is E_{8} for a description of the
E_{8} root system. This is a set of roots in R^{8}.
The 8 nodes of the Dynkin diagram correspond to 8 roots of the
E_{8} root system, which are a basis of the vector space.

This is a picture of the 248-dimensional Lie algebra of E_{8}.
This Lie algebra is a complex vector space, of dimension 248.
It is equipped with a Lie bracket operator: for X,Y in the Lie
algebra, so is [X,Y].
There are 248 nodes in the picture, one for each basis element of the
Lie algebra. Label the nodes 1,...,248, and the corresponding elements
of the Lie algebra Z_{1},...,Z_{248}.

The Lie algebra E_{8} is generated by 16 elements
X_{red},
Y_{red},
X_{blue},
Y_{blue},...,
X_{black},
Y_{black} corresponding to the nodes in the Dynkin
diagram.
These are elements of the Lie algebra, and
every element of the Lie algebra can be otained by taking brackets [,]
of these.

The Lie algebra of E_{8} is generated by 8 pairs of elements (X,Y),
one pair for each of the colored nodes in the Dynkin diagram.
Suppose a node in the big diagram does not have a red edge, for example. This means the
operators X and
Y take Z_{i} to a multiple of itself.
If node i is connected to node j by a red edge,
then X and Y take
Z_{i} to some linear combination of Z_{i} and Z_{j}.