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$C^*$-ALGEBRAS OF SELF-SIMILAR ACTION OF GROUPOIDS ON ROW-FINITE DIRECTED GRAPHS

Part of: Selfadjoint operator algebras

Published online by Cambridge University Press:  08 November 2022

ISNIE YUSNITHA Open the ORCID record for ISNIE YUSNITHA [Opens in a new window]
ISNIE YUSNITHA*
Affiliation:
School of Mathematics and Applied Statistics, University of Wollongong, Wollongong NSW 2522, Australia Department of Mathematics Education, Indonesia University of Education, West Java, Indonesia e-mail: [email protected]
*
e-mail: [email protected]
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Abstract

For amenable discrete groupoids $\mathcal {G}$ and row-finite directed graphs E, let $(\mathcal {G},E)$ be a self-similar groupoid and let $C^*(\mathcal {G}, E)$ be the associated $C^*$-algebra. We introduce a weaker faithfulness condition than those in the existing literature that still guarantees that $C^*(\mathcal {G})$ embeds in $C^*(\mathcal {G}, E)$. Under this faithfulness condition, we prove a gauge-invariant uniqueness theorem.

Keywords

row-finite graphsself-similar groupoidsinjectivity conditiongauge-invariant uniqueness theorem

MSC classification

Primary: 46L05: General theory of $C^*$-algebras
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 108 , Issue 1 , August 2023 , pp. 150 - 161
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Copyright
© The Author(s), 2022. Published by Cambridge University Press on behalf of Australian Mathematical Publishing Association Inc.

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Footnotes

This work is supported by a PhD scholarship of The Ministry of Education, Culture, Research and Technology of the Republic of Indonesia.

References

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