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PICARD GROUPS OF IRRATIONAL ROTATION C*-ALGEBRAS

Published online by Cambridge University Press:  01 August 1997

KAZUNORI KODAKA
KAZUNORI KODAKA
Affiliation:
Department of Mathematics, College of Science, Ryukyu University, Nishihara-cho, Okinawa, 903-01, Japan
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Abstract

Let θ be an irrational number in [0, 1] and Aθ the corresponding irrational rotation C*-algebra. Let Aut (Aθ) be the group of all automorphisms of Aθ and Int (Aθ) the normal subgroup of Aut (Aθ) of all inner automorphisms of Aθ. Let Pic (Aθ) be the Picard group of Aθ. In the present note we shall show that if θ is not quadratic, then Pic (Aθ)≅Aut (Aθ)/Int (Aθ) and that if θ is quadratic, then Pic (Aθ) is isomorphic to a semidirect product of Aut (Aθ)/Int (Aθ) with ℤ. Furthermore, in the last section we shall discuss Picard groups of certain Cuntz algebras.

Type
Research Article
Information
Journal of the London Mathematical Society , Volume 56 , Issue 1 , August 1997 , pp. 179 - 188
Copyright
The London Mathematical Society 1997

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