Abstract
This paper deals with two analytic questions on a connected compact Lie group G. i) Let a ∈ G and denote by γ the diffeomorphism of G given by γ (x) = ax (left translation by a). We give necessary and sufficient conditions for the existence of solutions of the cohomological equation f - f ∘ γ = g on the Fréchet space C∞ (G) of complex C∞ functions on G. ii) When G is the torus ${\Bbb T}^n$, we compute explicitly the distributions on ${\Bbb T}^n$ invariant by an affine automorphism γ, that is, γ (x) = A (x + a) with A ∈ GL(n, ℤ) and a ∈ ${\Bbb T}^n$. iii) We apply these results to describe the infinitesimal deformations of some Lie foliations.
Citation
Aziz EL KACIMI ALAOUI. Hadda HMILI. "Cohomological equations and invariant distributions on a compact Lie group." Hokkaido Math. J. 43 (2) 151 - 173, June 2014. https://doi.org/10.14492/hokmj/1404229920
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