Hopf Algebra - Cohomology of Lie Groups

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 × GG. 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

Other articles related to "cohomology of lie groups, cohomology, lie group, group, of lie groups":

Hopf Algebras - 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 ... Using this structure, Hopf proved a structure theorem for the cohomology algebra of Lie groups ...

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