This research demonstrates the equality of de Rham cohomology and Lie algebra cohomology in a Lie group context, indicating deep connections in algebraic topology.
Let H H be a dense subgroup of a Lie group G G with Lie algebra g {g} . We show that the (diffeological) de Rham cohomology of G / H G/H equals the Lie algebra cohomology of g / h {g}/{h} , where h {h} is the ideal { Z ∈ g : exp ( t Z ) ∈ H for all t ∈ R } \{Z∈ {g}:exp (tZ)∈ H for all t∈ { R}\} .
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Clark et al. (2026) studied this question.
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