spheres that are Lie groups
Theorem - The only spheres (http://planetmath.org/Sphere) that are Lie groups are , and .
Proof: It is known that , and have a Lie group .
On the other , we have seen in the parent entry (http://planetmath.org/CohomologyOfCompactConnectedLieGroups) that the cohomology groups (http://planetmath.org/DeRhamCohomology) of a compact connected Lie group satisfy
The result then follows from the fact that the of spheres satisfy and for .
|Title||spheres that are Lie groups|
|Date of creation||2013-03-22 17:50:02|
|Last modified on||2013-03-22 17:50:02|
|Last modified by||asteroid (17536)|