Manifolds of Lie-Group-Valued Cocycles and Discrete Cohomology

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2023
• Main Authors: Chirvasitu, Alexandru, Peng, Jun
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2023
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/212025
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: Manifolds of Lie-Group-Valued Cocycles and Discrete Cohomology. Alexandru Chirvasitu and Jun Peng. SIGMA 19 (2023), 106, 28 pages

Consider a compact group 𝐺 acting on a real or complex Banach Lie group 𝑈, by automorphisms in the relevant category, and leaving a central subgroup 𝛫 ≤ 𝑈 invariant. We define the spaces 𝛫𝑍ⁿ(𝐺, 𝑈) of 𝛫-relative continuous cocycles as those maps 𝐺ⁿ → 𝑈 whose coboundary is a 𝛫-valued (𝑛 + 1)-cocycle;...