On the existence of ergodic automorphisms in ergodic ℤd-actions on compact groups

Autor:	C. R. E. Raja
Rok vydání:	2009
Předmět:	Pure mathematics Group (mathematics) Applied Mathematics General Mathematics Metrization theorem Ergodicity Ergodic theory Finitely generated group Center (group theory) Abelian group Automorphism Mathematics
Zdroj:	Ergodic Theory and Dynamical Systems. 30:1803-1816
ISSN:	1469-4417 0143-3857
DOI:	10.1017/s0143385709000728
Popis:	Let K be a compact metrizable group and Γ be a finitely generated group of commuting automorphisms of K. We show that ergodicity of Γ implies Γ contains ergodic automorphisms if center of the action, Z(Γ)={α∈Aut(K)∣α commutes with elements of Γ} has descending chain condition. To explain that the condition on the center of the action is not restrictive, we discuss certain abelian groups which, in particular, provide new proofs to the theorems of Berend [Ergodic semigroups of epimorphisms. Trans. Amer. Math. Soc.289(1) (1985), 393–407] and Schmidt [Automorphisms of compact abelian groups and affine varieties. Proc. London Math. Soc. (3) 61 (1990), 480–496].
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::61ac76a70434bdb5d64e66dd22512c7a https://doi.org/10.1017/s0143385709000728 Zobrazit plný text záznamu