dc.contributor.author Conti, Roberto dc.contributor.author Hong, Jeong Hee dc.contributor.author Szymański, Wojciech dc.date.accessioned 2011-03-20T12:01:23Z dc.date.accessioned 2016-10-05T14:14:21Z dc.date.available 2011-03-20T12:01:23Z dc.date.available 2016-10-05T14:14:21Z dc.date.issued 2011-05-28 dc.identifier.uri http://publications.mfo.de/handle/mfo/1201 dc.description Research in Pairs 2011 en_US dc.description.abstract The 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.iso en en_US dc.publisher Mathematisches Forschungsinstitut Oberwolfach en_US dc.relation.ispartofseries Oberwolfach Preprints;2011,31 dc.subject Cuntz algebra en_US dc.subject MASA en_US dc.subject automorphism en_US dc.subject endomorphism en_US dc.subject Cantor set en_US dc.title The Weyl group of the Curtz algebra en_US dc.type Preprint en_US dc.identifier.doi 10.14760/OWP-2011-31 local.scientificprogram Research in Pairs 2011 local.series.id OWP-2011-31 local.subject.msc 46 local.subject.msc 37
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