Uniform rank metric stability of Lie algebras and groups

2024/08/28 by Benjamin Bachner, Bachner, Benjamin
Chemistry · Engineering · #FOS: Mathematics #Group Theory (math.GR) #Metal-Organic Frameworks: Synthesis and Applications #Stability and Control of Uncertain Systems

paper · pdf · doi:10.48550/arxiv.2408.15614

openalex publication_date 2024/08/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study uniform stability of discrete groups, Lie groups and Lie algebras in the rank metric, and the connections between uniform stability of these objects. We prove that semisimple Lie algebras are far from being flexibly ℂ-stable, and that semisimple Lie groups and lattices in semisimple Lie groups of higher rank are not strictly ℂ-stable. Furthermore, we prove that free groups are not uniformly flexibly F-stable over any field F.

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