2024/04/15 by Elyasheev Leibtag, Leibtag, Elyasheev
Mathematics · #20G05 #20G25 #20M99 #22E50 #43A99 #54D25 #54H11 #54H13 #Advanced Topics in Algebra #Advanced Topology and Set Theory #FOS: Mathematics #Group Theory (math.GR) #Mathematical Dynamics and Fractals
paper · pdf · doi:10.48550/arxiv.2404.09878
openalex publication_date 2024/04/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We show that for algebraic groups over local fields of characteristic zero, the following are equivalent: Every homomorphism has a closed image, every unitary representation decomposes into a direct sum of finite-dimensional and mixing representations, and that the matrix coefficients are dense within the algebra of weakly almost periodic functions over the group. In our proof, we employ methods from semi-group theory. We establish that algebraic groups are compactification-centric, meaning sG = Gs for any element s in the weakly almost periodic compactification of the group G.