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10 czerwca 2025 / June 10, 2025
Piotr M. Hajac (IM PAN)
Unital embeddings of C*-algebras that one can see
Abstract: Cuntz algebras 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 O_m in O_n whenever n-1 divides m-1. In 2009, Kawamura provided a simple and explicit formula for all such embeddings. It turns out that his formulas can be easily deduced by viewing Cuntz algebras as graph C*-algebras, known as operator algebras that one can see. Better still, playing the game of graphs and using both the covariant and contravariant functoriality of assigning graph C*-algebras to directed graphs, we can show how to embed Cuntz algebras into matrices over Cuntz algebras via straightforward polynomial formulas. Based on joint work with Yang Liu.