Subsystems of finite type and semigroup invariants of subshifts

• Verfasst von: Hamachi, Toshihiro [VerfasserIn]
• Verfasst von: Inoue, Kokoro [VerfasserIn]
• Verfasst von: Krieger, Wolfgang [VerfasserIn]
• Titel: Subsystems of finite type and semigroup invariants of subshifts
• Verf.angabe: by Toshihiro Hamachi and Kokoro Inoue at Fukuoka, and Wolfgang Krieger at Heidelberg
• Jahr: 2009
• Umfang: 25 S.
• Teil: year:2009
• Teil: number:632
• Teil: pages:37-61
• Teil: extent:25
• Fussnoten: Online erschienen: 16.06.2009 ; Gesehen am 21.06.2018
• Titel Quelle: Enthalten in: Journal für die reine und angewandte Mathematik
• Ort Quelle: Berlin : de Gruyter, 1826
• Jahr Quelle: 2009
• Band/Heft Quelle: (2009), 632, Seite 37-61
• ISSN Quelle: 1435-5345
• DOI: doi:10.1515/CRELLE.2009.049
• Datenträger: Online-Ressource
• Sprache: eng
• K10plus-PPN: 1576747239

Abstract

Hamachi and Inoue obtained a necessary and su‰cient condition for the embeddability of an irreducible subshift of finite type into a Dyck shift (Embedding of shifts of finite type into the Dyck shift, Monatsh. Math. 45 (2005), 107–129). Krieger introduced a property A of subshifts that is an invariant of topological conjugacy and he constructed for property A subshifts an invariantly associated semigroup (with zero) (On a syntactically defined invariant of symbolic dyanamics, Ergod. Th. Dynam. Sys. 20 (2000), 501–516). We introduce a class of property A subshifts, of which the Dyck shifts are prototypes, to which there are associated inverse semigroups (with zero) that arise from finite directed graphs. These subshifts also allow a suitable presentation by a finite directed graph that is labeled by elements of the associated inverse semigroup. We extend the criterion for embeddability of an irreducible subshift of finite type from the Dyck shifts to target shifts in this class.