In the mathematical fields of Lie theory and algebraic topology, the notion of Cartan pair is a technical condition on the relationship between a reductive Lie algebra and a subalgebra reductive in . A reductive pair is said to be Cartan if the relative Lie algebra cohomology is isomorphic to the tensor product of the characteristic subalgebra and an exterior subalgebra of , where On the level of Lie groups, if G is a compact, connected Lie group and K a closed connected subgroup, there are natural fiber bundles , .