Deformations of crossed homomorphisms on Lie groups

2025/12/15 by Jun Jiang, Jiang, Jun
Mathematics · #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Group Theory (math.GR) #Homotopy and Cohomology in Algebraic Topology #Rings and Algebras (math.RA)

paper · pdf · doi:10.48550/arxiv.2512.12973

openalex publication_date 2025/12/15 · openalex created_date 2025/12/17 · openalex updated_date 2026/07/28

Abstract

In this paper, we study deformations of crossed homomorphisms on Lie groups by means of the cohomology which controls them. Using the Moser type argument, we obtain several rigidity results of crossed homomorphisms on Lie groups. We further investigate the relationship between the cohomology of crossed homomorphisms on Lie groups and that on Lie algebras. Finally, we characterize the rigidity properties of all crossed homomorphisms with respect to the conjugation action on the connected and simply connected two-dimensional Lie group.

Citations

• Deformation maps of quasi-twilled Lie algebras
• Crossed homomorphisms and low dimensional representations of mapping class groups of surfaces
• Stability of Lie group homomorphisms and Lie subgroups

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