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On conjugacy of maximal abelian subalgebras and the outer automorphism group of the Cuntz algebra

Published online by Cambridge University Press:  02 April 2015

Roberto Conti ,
Jeong Hee Hong  and
Wojciech Szymański
Roberto Conti
Affiliation:
Dipartimento di Scienze di Base e Applicate per l’Ingegneria, Sezione di Matematica, Sapienza Università di Roma, Via A. Scarpa 16, 00161 Roma, Italy, (roberto.conti@sbai.uniroma1.it)
Jeong Hee Hong
Affiliation:
Department of Data Information, Korea Maritime and Ocean University, Busan 606–791, Republic of Korea, (hongjh@kmou.ac.kr)
Wojciech Szymański
Affiliation:
Department of Mathematics and Computer Science, University of Southern Denmark, Campusvej 55, 5230 Odense M, Denmark, (szymanski@imada.sdu.dk)
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Abstract

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We investigate the structure of the outer automorphism group of the Cuntz algebra and the closely related problem of conjugacy of maximal abelian subalgebras in . In particular, we exhibit an uncountable family of maximal abelian subalgebras, conjugate to the standard maximal abelian subalgebra via Bogolubov automorphisms, that are not inner conjugate to .

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 145 , Issue 2 , April 2015 , pp. 269 - 279
Copyright
Copyright © Royal Society of Edinburgh 2015