2022/07/25 by Benjamin Martin, Martin, Benjamin
Mathematics · #14L17 (Primary) #14L24 (Secondary) #Advanced Algebra and Geometry #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.2207.12169
openalex publication_date 2022/07/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The notion of a G-completely reducible subgroup is important in the study of algebraic groups and their subgroup structure. It generalizes the usual idea of complete reducibility from representation theory: a subgroup H of a general linear group G= \rm GLn(k) is G-completely reducible if and only if the inclusion map i\colon H→ \rm GLn(k) is a completely reducible representation of H. In these notes I give an introduction to the theory of complete reducibility and its applications, and explain an approach to the subject using geometric invariant theory.