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Endomorphisms of rational rotation C*-algebras

Published online by Cambridge University Press:  01 September 1999

P. J. STACEY
P. J. STACEY
Affiliation:
Department of Mathematics, La Trobe University, Bundoora, Victoria 3083, Australia. e-mail: p.stacey@latrobe.edu.au
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Abstract

Let Aθ be the universal C*-algebra generated by a pair U, V of unitaries satisfying VU = e2πiθUV where θ = p/q with p, q∈ℤ, 0 < p < q and (p, q) = 1. It is shown that every endomorphism of Aθ is unital, injective and centre preserving. The corresponding surjections of T2 are characterized and it is shown that the determinants of the associated endomorphisms of K1(Aθ)≅ℤ2 are congruent to 1 modulo q.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 127 , Issue 2 , September 1999 , pp. 289 - 294
Copyright
The Cambridge Philosophical Society 1999

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