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2011 | 96 | 1 | 81-97
Tytuł artykułu

Endomorphisms of the Cuntz algebras

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Języki publikacji
EN
Abstrakty
EN
This mainly expository article is devoted to recent advances in the study of dynamical aspects of the Cuntz algebras 𝓞ₙ, n < ∞, via their automorphisms and, more generally, endomorphisms. A combinatorial description of permutative automorphisms of 𝓞ₙ in terms of labelled, rooted trees is presented. This in turn gives rise to an algebraic characterization of the restricted Weyl group of 𝓞ₙ. It is shown how this group is related to certain classical dynamical systems on the Cantor set. An identification of the image in Out(𝓞ₙ) of the restricted Weyl group with the group of automorphisms of the full two-sided n-shift is given, for prime n, providing an answer to a question raised by Cuntz in 1980. Furthermore, we discuss proper endomorphisms of 𝓞ₙ which preserve either the canonical UHF-subalgebra or the diagonal MASA, and present methods for constructing exotic examples of such endomorphisms.
Słowa kluczowe
Rocznik
Tom
96
Numer
1
Strony
81-97
Opis fizyczny
Daty
wydano
2011
Twórcy
  • Dipartimento di Scienze di Base e Applicate per l'Ingegneria, Sezione di Matematica, Sapienza Università di Roma, Via A. Scarpa 16, 00161 Roma, Italy
  • Department of Data Information, Korea Maritime University, Busan 606-791, South Korea
  • Department of Mathematics and Computer Science, The University of Southern Denmark, Campusvej 55, DK-5230 Odense M, Denmark
Bibliografia
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-doi-10_4064-bc96-0-5
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