Journal of Operator Theory

Volume 46, Issue 3, Supplementary 2001 pp. 561-577.

Endomorphisms of continuous Cuntz algebras

Authors: Joachim Zacharias
Author institution: University of Nottingham, School of Mathematical Sciences, University Park, Nottingham NG7 2RD, England

Summary: We establish a one to one correspondence between endomorphisms of Arveson's continuous analogues $\CSE$ of the Cuntz algebras and certain cocycles. For the analogues of quasi-free automorphism groups there are no positive gauge invariant KMS-weights, whereas for the gauge action there exists a non lower semi-continuous ground weight on $C^*(E)$. Crossed products by quasi-free actions are often simple.

Keywords: Continuous Cuntz algebras (spectral algebras), endomorphisms, quasi-free automorphisms

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