Analysis of Endomorphisms

Research output: Contribution to journalConference articleResearchpeer-review

Abstract

In this expository article, we discuss the recent progress in the study of endomorphisms and automorphisms of the Cuntz algebras and, more generally graph C*-algebras (or Cuntz-Krieger algebras). In particular, we discuss the definition and properties of both the full and the restricted Weyl group of such an algebra. Then we outline a powerful combinatorial approach to analysis of endomorphisms arising from permutation unitaries. The restricted Weyl group consists of automorphisms of this type. We also discuss the action of the restricted Weyl group on the diagonal MASA and its relationship with the automorphism group of the full two-sided n-shift. Finally, several open problems are presented.
Original languageEnglish
Book seriesJournal of Physics: Conference Series (Online)
Volume346
Issue number1
Pages (from-to)1-7
Number of pages7
ISSN1742-6596
DOIs
Publication statusPublished - 2012

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automorphisms
algebra
permutations
shift

Keywords

  • Cuntz algebra
  • endomorphism
  • C*-algebra

Cite this

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title = "Analysis of Endomorphisms",
abstract = "In this expository article, we discuss the recent progress in the study of endomorphisms and automorphisms of the Cuntz algebras and, more generally graph C*-algebras (or Cuntz-Krieger algebras). In particular, we discuss the definition and properties of both the full and the restricted Weyl group of such an algebra. Then we outline a powerful combinatorial approach to analysis of endomorphisms arising from permutation unitaries. The restricted Weyl group consists of automorphisms of this type. We also discuss the action of the restricted Weyl group on the diagonal MASA and its relationship with the automorphism group of the full two-sided n-shift. Finally, several open problems are presented.",
keywords = "Cuntz algebra, endomorphism, C*-algebra",
author = "Roberto Conti and Hong, {Jeong Hee} and Wojciech Szymanski",
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language = "English",
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}

Analysis of Endomorphisms. / Conti, Roberto; Hong, Jeong Hee; Szymanski, Wojciech.

In: Journal of Physics: Conference Series (Online), Vol. 346, No. 1, 2012, p. 1-7.

Research output: Contribution to journalConference articleResearchpeer-review

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T1 - Analysis of Endomorphisms

AU - Conti, Roberto

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AU - Szymanski, Wojciech

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N2 - In this expository article, we discuss the recent progress in the study of endomorphisms and automorphisms of the Cuntz algebras and, more generally graph C*-algebras (or Cuntz-Krieger algebras). In particular, we discuss the definition and properties of both the full and the restricted Weyl group of such an algebra. Then we outline a powerful combinatorial approach to analysis of endomorphisms arising from permutation unitaries. The restricted Weyl group consists of automorphisms of this type. We also discuss the action of the restricted Weyl group on the diagonal MASA and its relationship with the automorphism group of the full two-sided n-shift. Finally, several open problems are presented.

AB - In this expository article, we discuss the recent progress in the study of endomorphisms and automorphisms of the Cuntz algebras and, more generally graph C*-algebras (or Cuntz-Krieger algebras). In particular, we discuss the definition and properties of both the full and the restricted Weyl group of such an algebra. Then we outline a powerful combinatorial approach to analysis of endomorphisms arising from permutation unitaries. The restricted Weyl group consists of automorphisms of this type. We also discuss the action of the restricted Weyl group on the diagonal MASA and its relationship with the automorphism group of the full two-sided n-shift. Finally, several open problems are presented.

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