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Toral automorphisms and antiautomorphisms of rotation algebras

Published online by Cambridge University Press:  17 April 2009

Hu Yaohua  and
P.J. Stacey
Hu Yaohua
Affiliation:
School of Mathematics, La Trobe University, Bundoora Vic 3083, Australia e-mail: matyh@lure.latrobe.edu.au
P.J. Stacey
Affiliation:
School of Mathematics, La Trobe University, Bundoora Vic 3083, Australia e-mail: P.Stacey@latrobe.edu.au
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Abstract

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If U, V are the generators of a rational or irrational rotation C*-algebra then an automorphism φ of the algebra is determined by φ(U) = λUaVc and φ(V) = μUbVd where λ, μ are complex numbers of modulus 1 and a, b, c, d are integers with ad − bc = 1. If ad − bc = −1, then these formulae determine an antiautomorphsm of the algebra. The classification of such automorphisms and antiautomorphisms up to conjugacy by arbitrary automorphisms is studied and an almost complete classification is obtained.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 59 , Issue 2 , April 1999 , pp. 247 - 255
Copyright
Copyright © Australian Mathematical Society 1999

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