Unital embeddings of Cuntz algebras from path homomorphisms of graphs
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866929721838665728 |
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| author | Hajac, Piotr M. Liu, Yang |
| author_facet | Hajac, Piotr M. Liu, Yang |
| contents | Cuntz algebras $\mathcal{O}_n$, $n>1$, are celebrated examples of a separable infinite simple C*-algebra with a number of fascinating properties. Their K-theory allows an embedding of $\mathcal O_m$ in $\mathcal O_n$ whenever $n-1$ divides $m-1$. In 2009, Kawamura provided a simple and explicit formula for all such embeddings. His formulas can be easily deduced by viewing Cuntz algebras as graph C*-algebras. Our main result is that, using both the covariant and contravariant functoriality of assigning graph C*-algebras to directed graphs, we can provide explicit polynomial formulas for all unital embeddings of Cuntz algebras into matrices over Cuntz algebras allowed by K-theory. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_17167 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Unital embeddings of Cuntz algebras from path homomorphisms of graphs Hajac, Piotr M. Liu, Yang Operator Algebras Cuntz algebras $\mathcal{O}_n$, $n>1$, are celebrated examples of a separable infinite simple C*-algebra with a number of fascinating properties. Their K-theory allows an embedding of $\mathcal O_m$ in $\mathcal O_n$ whenever $n-1$ divides $m-1$. In 2009, Kawamura provided a simple and explicit formula for all such embeddings. His formulas can be easily deduced by viewing Cuntz algebras as graph C*-algebras. Our main result is that, using both the covariant and contravariant functoriality of assigning graph C*-algebras to directed graphs, we can provide explicit polynomial formulas for all unital embeddings of Cuntz algebras into matrices over Cuntz algebras allowed by K-theory. |
| title | Unital embeddings of Cuntz algebras from path homomorphisms of graphs |
| topic | Operator Algebras |
| url | https://arxiv.org/abs/2412.17167 |