The Weyl group of the Cuntz algebra

dc.bibliographicCitation.seriesTitleOberwolfach Preprints (OWP)eng
dc.bibliographicCitation.volume2011-31
dc.contributor.authorConti, Roberto
dc.contributor.authorHong, Jeong Hee
dc.contributor.authorSzyma´nski, Wojciech
dc.date.available2019-06-28T08:04:46Z
dc.date.issued2011
dc.description.abstractThe Weyl group of the Cuntz algebra On is investigated. This is (isomorphic to) the group of polynomial automorphisms λu of On, namely those induced by unitaries u that can be written as finite sums of words in the canonical generating isometries Si and their adjoints. A necessary and sufficient algorithmic combinatorial condition is found for deciding when a polynomial endomorphism λu restricts to an automorphism of the canonical diagonal MASA. Some steps towards a general criterion for invertibility of λu on the whole of On are also taken. A condition for verifying invertibility of a certain subclass of polynomial endomorphisms is given. First examples of polynomial automorphisms of On not inner related to permutative ones are exhibited, for every n≥2. In particular, the image of the Weyl group in the outer automorphism group of On is strictly larger than the image of the reduced Weyl group analyzed in previous papers. Results about the action of the Weyl group on the spectrum of the diagonal are also included.eng
dc.description.versionpublishedVersioneng
dc.formatapplication/pdf
dc.identifier.issn1864-7596
dc.identifier.urihttps://doi.org/10.34657/3393
dc.identifier.urihttps://oa.tib.eu/renate/handle/123456789/2229
dc.language.isoengeng
dc.publisherOberwolfach : Mathematisches Forschungsinstitut Oberwolfacheng
dc.relation.doihttps://doi.org/10.14760/OWP-2011-31
dc.rights.licenseThis document may be downloaded, read, stored and printed for your own use within the limits of § 53 UrhG but it may not be distributed via the internet or passed on to external parties.eng
dc.rights.licenseDieses Dokument darf im Rahmen von § 53 UrhG zum eigenen Gebrauch kostenfrei heruntergeladen, gelesen, gespeichert und ausgedruckt, aber nicht im Internet bereitgestellt oder an Außenstehende weitergegeben werden.ger
dc.subject.ddc510eng
dc.subject.otherCuntz-Krieger algebraeng
dc.subject.othergraph algebraeng
dc.subject.otherendomorphismeng
dc.subject.otherautomorphismeng
dc.subject.otherCantor seteng
dc.titleThe Weyl group of the Cuntz algebraeng
dc.typeReporteng
dc.typeTexteng
tib.accessRightsopenAccesseng
wgl.contributorMFOeng
wgl.subjectMathematikeng
wgl.typeReport / Forschungsbericht / Arbeitspapiereng
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