You should check out Theodore Frankel's Geometry of Physics. There is a section on the gauge group . The cartan three form is the three form from the Chern Simons term at a flat connection. A flat connection is when the potential A is equal to the $g^{-1}dg$. In the Chern Simons 3 form you have A^A^A. At pure gauge this becomes $Tr(g^{-1}dg\wedge g^{-1}dg\wedge g^{-1}dg)$. This term is proportional to the cartan 3 form. I hope this helped.
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