Automorphisms of the Cuntz algebras

Roberto Conti, Wojciech Szymanski

Research output: Chapter in Book/Report/Conference proceedingArticle in proceedingsResearchpeer-review

Abstract

We survey recent results on endomorphisms and especially on automorphisms of the Cuntz algebras, with a special emphasis on the structure of the Weyl group. We discuss endomorphisms globally preserving the diagonal MASA and their corresponding actions. In particular, we investigate those endomorphisms of O_n which restrict to automorphisms of the diagonal. We review a combinatorial approach to the study of permutative endomorphisms. All the presented material is put in context with current research topics.
Original languageEnglish
Title of host publicationProgress in operator algebras, noncommutative geometry, and their applications : Proceedings of the 4th annual meeting of the European Noncommutative Geometry Network, Bucharest, April 25-30, 2011
EditorsIonel Popescu, Radu Purice
Place of PublicationBucharest
PublisherTheta
Publication date2012
Pages1-15
ISBN (Print)978-606-8443-01-0
Publication statusPublished - 2012
SeriesTheta Series in Advanced Mathematics

Keywords

  • Cuntz algebra
  • endomorphism
  • automorphism
  • Cartan subalgebra
  • core UHF-subalgebra
  • normalizer
  • Weyl group
  • permutation
  • tree
  • shift

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