spheres that are Lie groups


spheres \PMlinkescapephrasesatisfy

Theorem - The only spheres (http://planetmath.org/Sphere) that are Lie groupsMathworldPlanetmath are S0, S1 and S3.

Proof: It is known that S0, S1 and S3 have a Lie group .

On the other , we have seen in the parent entry (http://planetmath.org/CohomologyOfCompactConnectedLieGroups) that the cohomology groupsPlanetmathPlanetmath (http://planetmath.org/DeRhamCohomology) of a compact connected Lie group G satisfy


The result then follows from the fact that the of spheres satisfy H1(Sn;)=0 and H3(Sn;)=0 for n1,3.

Title spheres that are Lie groups
Canonical name SpheresThatAreLieGroups
Date of creation 2013-03-22 17:50:02
Last modified on 2013-03-22 17:50:02
Owner asteroid (17536)
Last modified by asteroid (17536)
Numerical id 7
Author asteroid (17536)
Entry type Corollary
Classification msc 22E99
Classification msc 57T10