Localized Automorphisms and Endomorphisms

Authors

  • Abdelgabar Adam Hassan Department of Mathematics, College of Science, Jouf University, Kingdom of Saudi Arabia; Department of Mathematics, University of Nyala, Nyala, Sudan https://orcid.org/0000-0001-6233-2332

DOI:

https://doi.org/10.26713/cma.v14i5.1971

Keywords:

Algebra, Endomorphism, Automorphism, Uniformly hyperfinite, Cuntz algebra

Abstract

We give a practical criterion of invertibility of endomorphisms of \(O_n\) corresponding to unitaries in the normalizer of the diagonal inside the uniformly hyperfinite subalgebra. We also analyze the action of such localized automorphisms on the spectrum of the diagonal thus obtaining criteria of outerness. Unital endomorphisms of the Cuntz algebra \(O_n\) which preserve the canonical uniformly hyperfinite-subalgebra \(F_n \subseteq O_n\) are investigated. We give examples of such endomorphisms \(\lambda =\lambda_u\) for which the associated unitary element \(u\) in \(O_n\).

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Published

31-12-2023
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How to Cite

Hassan, A. A. (2023). Localized Automorphisms and Endomorphisms. Communications in Mathematics and Applications, 14(5), 1575–1584. https://doi.org/10.26713/cma.v14i5.1971

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Research Article