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The generator rank of C*-algebras

Thiel, Hannes...

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The generator rank of C*-algebras by Thiel, Hannes ( Author )

Content Provider	Lemonjar Open Access
Publisher	Australian National University
Publication Date	11-08-2023
Summary	We show that every AF-algebra is generated by a single operator. This was previously unclear, since the invariant that assigns to a C-algebra its minimal number of generators lacks natural permanence properties. In particular, it may increase when passing to ideals or inductive limits. To obtain a better behaved theory, we not only ask if a C-algebra is generated by $n$ elements, but also if generating $n$-tuples are dense. This defines the generator rank, which we show has many natural permanence properties: it does not increase when passing to ideals, quotients or inductive limits.
ISBN	-
Item Type	Article
File Type	pdf
File Size	30.00 KB
Language	English
Subjects	-
Unlimited	MYR 0.01
Total read	-
URL	http://arxiv.org/abs/1210.6608

Citation

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AMA 11th EditionReferences

Thiel, Hannes. The generator rank of C*-algebras. Australian National University. August 11, 2023. Accessed October 02, 2025. https://online.provdatabase.com/cite/16020

APA 7th EditionReferences

Thiel, Hannes. (2023). The generator rank of C*-algebras. Australian National University. https://online.provdatabase.com/cite/16020

Chicago 17th EditionReferences

Thiel, Hannes. The generator rank of C*-algebras. Australian National University. 2023. https://online.provdatabase.com/cite/16020

HarvardReferences

Thiel, Hannes. (2023). The generator rank of C*-algebras. [Online]. Australian National University. Available from: https://online.provdatabase.com/cite/16020. (Accessed 02 October 2025).

Harvard AustraliaReferences

Thiel, Hannes, 2023, The generator rank of C*-algebras, Australian National University, viewed 02 October 2025, <https://online.provdatabase.com/cite/16020>

MLA 9th EditionWorks Cited

Thiel, Hannes. The generator rank of C*-algebras. Australian National University, 2023. PROV Database, https://online.provdatabase.com/cite/16020.

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