2022/09/15 by М. В. Нещадим, Neshchadim, Mikhail V., Andrey A. Simonov +1
Mathematics · #18F60 #20B22 #22A30 #22A99 #Advanced Topics in Algebra #FOS: Mathematics #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.2209.07425
openalex publication_date 2022/09/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The paper is devoted to generalizations of actions of topological groups on manifolds. Instead of a topological group, we consider a local topological group generalizing the notion of a~germ or a~neighborhood in a topological group. The notion of an action of a local group on a topological space is introduced. The paper constructs the theory of local sharply n-transitive groups and local n-pseudofields. Local sharply n-transitive groups are reduced to simpler algebraic objects -- local n-pseudofields, similarly to the way Lie groups are reduced to Lie algebras, and sharply two-transitive groups, are reduced to neardomains. This can be useful, since, opposite to locally compact and connected sharply n-transitive groups, which are absent for n > 3, local sharply n-transitive groups exist for any n, for example, the group GLn(ℝ). Being boundedly sharply n-transitive, the groups under consideration are also Lie groups, which gives extra methods for their study.