Journal of Lie Theory

no. 3
Straightening Banach-Lie-Group-Valued Almost-Cocycles
Journal of Lie Theory, Volume 35 (2025) no. 3, pp. 447-453

For a compact group $$\mathbb{G}$$ acting continuously on a Banach Lie group $$\mathbb{U}$$, we prove that maps $$\mathbb{G}\to \mathbb{U}$$ close to being 1-cocycles for the action can be deformed analytically into actual 1-cocycles. This recovers Hyers-Ulam stability results of Grove-Karcher-Ruh (trivial $$\mathbb{G}$$-action, compact Lie $$\mathbb{G}$$ and $$\mathbb{U}$$) and de la Harpe-Karoubi (trivial $$\mathbb{G}$$-action, $$\mathbb{U}:=$$invertible elements of a Banach algebra). The obvious analogues for higher cocycles also hold for abelian $$\mathbb{U}$$.

Received:
Revised:
Accepted:
DOI: 10.5802/jolt.1392
Keywords: 22E65, 22C05, 58B25, 46E50, 20J06, 58C15, 22E66, 22D12, 39B82, 46G20, 22E41, Banach Lie group, cocycle, coboundary, Haar measure, averaging, almost-morphism, Baker-Campbell-Hausdorff, Hyers-Ulam-Rassias stability 
@article{JOLT_2025_35_3_a0,
     author = {A. Chirvasitu},
     title = {Straightening {Banach-Lie-Group-Valued} {Almost-Cocycles
}},
     journal = {Journal of Lie Theory},
     pages = {447--453},
     year = {2025},
     volume = {35},
     number = {3},
     doi = {10.5802/jolt.1392},
     zbl = {08103097},
     language = {en},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.1392/}
}
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A. Chirvasitu. Straightening Banach-Lie-Group-Valued Almost-Cocycles. Journal of Lie Theory, Volume 35 (2025) no. 3, pp. 447-453. doi: 10.5802/jolt.1392

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