Endomorphisms of certain irrational rotation \(C^*\)-algebras
type: Item
instance of: scholarly article
title: Endomorphisms of certain irrational rotation \(C^*\)-algebras
zbMATH Open document ID: 0760.46056
author: Kazunori Kodaka
published in: Illinois Journal of Mathematics
publication date: 1993-02-10T00:00:00Z
review text: Let \(\theta\) be a quadratic irrational number with its discriminant \(D=5\). Let \(A_ \theta\) be the corresponding irrational rotation \(C^*\)-algebra. In the present paper we construct a unital endomorphism \(\Phi\) of \(A_ \theta\) with \(\Phi_ *\) an arbitrary endomorphism of \(K_ 1(A_ \theta)\). Furthermore we show that there is a unital endomorphism \(\varphi\) of \(A_ \theta\) with the minimizing index \([A_ \theta\): \(\varphi(A_ \theta)]_ 0=4\).
Mathematics Subject Classification ID: 46L55
Mathematics Subject Classification ID: 46L80
zbMATH DE Number: 119923
zbMATH Keywords: \(K_ 1\)-group
zbMATH Keywords: index for \(C^*\)-subalgebra
zbMATH Keywords: quadratic irrational number
zbMATH Keywords: irrational rotation \(C^*\)-algebra
zbMATH Keywords: unital endomorphism
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 119923