eprintid: 5829
rev_number: 9
eprint_status: archive
userid: 1
dir: disk0/00/00/58/29
datestamp: 2005-09-29 13:51:09
lastmod: 2015-04-25 07:39:05
status_changed: 2012-08-14 15:16:16
type: preprint
metadata_visibility: show
creators_name: Schraudner, Michael H.
title: Countable state Markov shifts with automorphism groups being a direct sum
ispublished: pub
subjects: ddc-510
divisions: i-110400
keywords: Subshift, (FMDP)-Graphen, Ausgeduennte Graphen, SFT, Kodierte Systemedirect sum, thinned out graph, (FMDP)-graph, SFT, coded system
cterms_swd: Topologische Markov-Kette
cterms_swd: Irreduzible Markov-Kette
cterms_swd: Automorphismengruppe
cterms_swd: Direkte Zerlegung
note: to appear as a shortened and modified version in \'Ergodic Theory and Dynamical Systems\' 
abstract: In this short note we prove the existence of a class of transitive, locally compact, countable state Markov shifts whose automorphism groups split into a direct sum of two groups; one being the infinite cyclic group generated by the shift map, the other being a countably infinite, centerless group $H$, which contains all automorphisms that act on the orbit-complement of certain finite sets of symbols like the identity. Such a decomposition is well known from the automorphism groups of coded systems, in which case one can explicitly construct example subshifts with $\aut(\sigma)=\seq{\sigma}\oplus H$ to a variety of abstract groups $H$. A similar result for shifts of finite type (SFTs) is yet only established for full $p$-shifts ($p$ prime), where $H$ equals the set of inert automorphisms. For general SFTs no direct sum representation is known so far. Thus our result may help to distinguish between the countable automorphism groups of SFTs and those of countable state Markov shifts.
abstract_translated_lang: eng
class_scheme: msc
class_labels: 37B10
date: 2005
date_type: published
id_scheme: DOI
id_number: 10.11588/heidok.00005829
ppn_swb: 1644180715
own_urn: urn:nbn:de:bsz:16-opus-58293
language: eng
bibsort: SCHRAUDNERCOUNTABLES2005
full_text_status: public
citation:   Schraudner, Michael H.  (2005) Countable state Markov shifts with automorphism groups being a direct sum.  [Preprint]     
document_url: https://archiv.ub.uni-heidelberg.de/volltextserver/5829/1/DIRECSUM.pdf