Unital embeddings of Cuntz algebras from path homomorphisms of graphs

Piotr M. Hajac; Yang Liu

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arXiv · 2412.17167

Unital embeddings of Cuntz algebras from path homomorphisms of graphs

Piotr M. Hajac·Yang Liu

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Abstract

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.

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BibTeX RIS

Piotr M. Hajac, Yang Liu. 2025-02-20. Unital embeddings of Cuntz algebras from path homomorphisms of graphs. https://arxiv.org/abs/2412.17167

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