Toral automorphisms and antiautomorphisms of rotation algebras

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...

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Bibliographic Details
Published in:Bulletin of the Australian Mathematical Society 1999-04, Vol.59 (2), p.247-255
Main Authors: Yaohua, Hu, Stacey, P.J.
Format: Article
Language:English
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Summary: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.
ISSN:0004-9727
1755-1633
DOI:10.1017/S000497270003286X