Decompositions of the automorphism group of a locally compact abelian group

Autor:	Smythe, Iian B.
Rok vydání:	2011
Předmět:	Mathematics - General Topology Mathematics - Category Theory Mathematics - Group Theory 22D45 22B05 (Primary) 54H11 18E05 20K30 (Secondary)
Druh dokumentu:	Working Paper
Popis:	It is well known that every locally compact abelian group L can be decomposed as L_1 \oplus R^n, where L_1 contains a compact-open subgroup. In this paper, we use this decomposition to study the topological group Aut(L) of automorphisms of L, equipped with the g-topology. We show that Aut(L) is topologically isomorphic to a matrix group with entries from Aut(L_1), Hom(L_1, R^n), Hom(R^n, L_1), and GL_n(R), respectively. It is also shown that the algebraic portion of the decomposition is not specific to locally compact abelian groups, but is also true for objects with a well-behaved decomposition in an additive category with kernels. Comment: 11 pages, 1 figure. First version of paper, comments are appreciated
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1110.1923 Zobrazit plný text záznamu View this record from Arxiv