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Journal für die reine und angewandte Mathematik

Managing Editor: Weissauer, Rainer

Ed. by Colding, Tobias / Huybrechts, Daniel / Hwang, Jun-Muk / Williamson, Geordie

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Volume 2012, Issue 667


The restricted Weyl group of the Cuntz algebra and shift endomorphisms

Roberto Conti
  • Dipartimento di Scienze, Università di Chieti-Pescara ‘G. D'Annunzio’, Viale Pindaro 42, 65127 Pescara, Italy
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/ Jeong Hee Hong / Wojciech Szymański
  • Department of Mathematics and Computer Science, The University of Southern Denmark, Campusvej 55, 5230 Odense M, Denmark
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Published Online: 2011-07-24 | DOI: https://doi.org/10.1515/CRELLE.2011.125


It is shown that, modulo the automorphisms which fix the canonical diagonal MASA point-wise, the group of those automorphisms of 𝒪n which globally preserve both the diagonal and the core UHF-subalgebra is isomorphic, via restriction, with the group of those homeomorphisms of the full one-sided n-shift space which eventually commute along with their inverses with the shift transformation. The image of this group in the outer automorphism group of 𝒪n can be embedded into the quotient of the automorphism group of the full two-sided n-shift by its center, generated by the shift. If n is prime then this embedding is an isomorphism.

About the article

Received: 2010-06-24

Revised: 2010-12-01

Published Online: 2011-07-24

Published in Print: 2012-06-01

Citation Information: Journal für die reine und angewandte Mathematik (Crelles Journal), Volume 2012, Issue 667, Pages 177–191, ISSN (Online) 1435-5345, ISSN (Print) 0075-4102, DOI: https://doi.org/10.1515/CRELLE.2011.125.

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