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dc.contributor.authorConti, Roberto
dc.contributor.authorHong, Jeong Hee
dc.contributor.authorSzymański, Wojciech
dc.date.accessioned2011-03-20T12:01:23Z
dc.date.accessioned2016-10-05T14:14:21Z
dc.date.available2011-03-20T12:01:23Z
dc.date.available2016-10-05T14:14:21Z
dc.date.issued2011-05-28
dc.identifier.urihttp://publications.mfo.de/handle/mfo/1201
dc.descriptionResearch in Pairs 2011en_US
dc.description.abstractThe Weyl group of the Cuntz algebra $\mathcal{O}_n$ is investigated. This is (isomorphic to) the group of polynomial automorphisms $\lambda_u$ of $\mathcal{O}_n$, namely those induced by unitaries u that can be written as finite sums of words in the canonical generating isometries $S_i$ and their adjoints. A necessary and sufficient algorithmic combinatorial condition is found for deciding when a polynomial endomorphism $\lambda_u$ restricts to an automorphism of the canonical diagonal MASA. Some steps towards a general criterion for invertibility of $\lambda_u$ on the whole of $\mathcal{O}_n$ are also taken. A condition for verifying invertibility of a certain subclass of polynomial endomorphisms is given. First examples of polynomial automorphisms of $\mathcal{O}_n$ not inner related to permutative ones are exhibited, for every $n\geq 2$. In particular, the image of the Weyl group in the outer automorphism group of $\mathcal{O}_n$ 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.en_US
dc.language.isoenen_US
dc.publisherMathematisches Forschungsinstitut Oberwolfachen_US
dc.relation.ispartofseriesOberwolfach Preprints;2011,31
dc.subjectCuntz algebraen_US
dc.subjectMASAen_US
dc.subjectautomorphismen_US
dc.subjectendomorphismen_US
dc.subjectCantor seten_US
dc.titleThe Weyl group of the Curtz algebraen_US
dc.typePreprinten_US
dc.identifier.doi10.14760/OWP-2011-31
local.scientificprogramResearch in Pairs 2011
local.series.idOWP-2011-31
local.subject.msc46
local.subject.msc37


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