claim: Northwestern University is a founding member of the Big Ten Conference starting in 1893.
evidence: 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 .. mathematical. mathematics. Lie theory. Lie theory. algebraic topology. algebraic topology. reductive Lie algebra. reductive Lie algebra. A reductive pair is said to be Cartan if the relative Lie algebra cohomology. Lie algebra cohomology. Lie algebra cohomology. is isomorphic to the tensor product of the characteristic subalgebra. and an exterior subalgebra of , where. , the Samelson subspace , are those primitive elements in the kernel of the composition ,. is the primitive subspace of ,. is the transgression ,. transgression. transgression map. and the map of symmetric algebras is induced by the restriction map of dual vector spaces .. 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. Lie groups. Lie groups. where. is the homotopy quotient , here homotopy equivalent to the regular quotient , and. homotopy quotient. Universal bundle#Use in the study of group actions. homotopy equivalent. homotopy equivalent. Then the characteristic algebra is the image of , the transgression from the primitive subspace P of is that arising from the edge maps in the Serre spectral sequence of the universal bundle , and the subspace of is the kernel of .. transgression. transgression map. Serre spectral sequence. Serre spectral sequence. universal bundle. universal bundle