Extensible endomorphisms of compact groups

Autor:	Chirvasitu, Alexandru
Rok vydání:	2023
Předmět:	Mathematics - Group Theory Mathematics - Category Theory Mathematics - Representation Theory 22C05 22D35 22D45 20K30 20J06 20K27 20C25 20K40 20K35 20K45 20G41
Druh dokumentu:	Working Paper
Popis:	We show that the endomorphisms of a compact connected group that extend to endomorphisms of every compact overgroup are precisely the trivial one and the inner automorphisms; this is an analogue, for compact connected groups, of results due to Schupp and Pettet on discrete groups (plain or finite). A somewhat more surprising result is that if $\mathbb{A}$ is compact connected and abelian, its endomorphisms extensible along morphisms into compact connected groups also include $-\mathrm{id}$ (in addition to the obvious trivial endomorphism and the identity). Connectedness cannot be dropped on either side in this last statement. Comment: 14 pages + references; v2 fixes a typo (resulting in a misstatement)
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2309.12791 Zobrazit plný text záznamu View this record from Arxiv