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Journal Articles Hokkaido Mathematical Journal Year : 2014

Cohomological equations and invariant distributions on a compact Lie group

Abstract

This paper deals with two analytic questions on a connected compact Lie group G. i) Let a ε 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 - fo γ = g on the Fréchet space C∞(G) of complex C∞ functions on G. ii) When G is the torus Tn, we compute explicitly the distributions on Tn invariant by an affine automorphism γ, that is, γ(x) = A(x + a) with A ε GL(n; ℤ) and a ε Tn. iii) We apply these results to describe the infinitesimal deformations of some Lie foliations.

Dates and versions

hal-03164536 , version 1 (10-03-2021)

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Cite

Aziz El Kacimi Alaoui, Hadda Hmili. Cohomological equations and invariant distributions on a compact Lie group. Hokkaido Mathematical Journal, 2014, 43 (2), pp.151-173. ⟨10.14492/hokmj/1404229920⟩. ⟨hal-03164536⟩
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