Construction
There are two ways to construct the monster Lie algebra. As it is a generalized Kac–Moody algebra whose simple roots are known, it can be defined by explicit generators and relations; however, this presentation does not give an action of the monster group on it.
It can also be constructed from the monster vertex algebra by using the Goddard–Thorn theorem of string theory. This construction is much harder, but has the advantage of proving that the monster group acts naturally on it.
Read more about this topic: Monster Lie Algebra
Famous quotes containing the word construction:
“No real “vital” character in fiction is altogether a conscious construction of the author. On the contrary, it may be a sort of parasitic growth upon the author’s personality, developing by internal necessity as much as by external addition.”
—T.S. (Thomas Stearns)
“There’s no art
To find the mind’s construction in the face.”
—William Shakespeare (1564–1616)
“There’s no art
To find the mind’s construction in the face:
He was a gentleman on whom I built
An absolute trust.”
—William Shakespeare (1564–1616)