Cohomology of Lie Groups
The cohomology algebra of a Lie group is a Hopf algebra: the multiplication is provided by the cup-product, and the comultiplication
by the group multiplication G × G → G. This observation was actually a source of the notion of Hopf algebra. Using this structure, Hopf proved a structure theorem for the cohomology algebra of Lie groups.
Theorem (Hopf) Let A be a finite-dimensional, graded commutative, graded cocommutative Hopf algebra over a field of characteristic 0. Then A (as an algebra) is a free exterior algebra with generators of odd degree.
Read more about this topic: Hopf Algebra
Famous quotes containing the words lie and/or groups:
“Any fool can tell the truth, but it requires a man of some sense to know how to lie well.”
—Samuel Butler (18351902)
“Writers and politicians are natural rivals. Both groups try to make the world in their own images; they fight for the same territory.”
—Salman Rushdie (b. 1947)