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arXiv · 2407.21582

Non-linear classification of finite-dimensional simple $C^*$-algebras

Bojan Kuzma·Sushil Singla
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Abstract

A Banach space characterization of simple real or complex $C^*$-algebras is given which even characterizes the underlying field. As an application, it is shown that if $\mathfrak A_1$ and $\mathfrak A_2$ are Birkhoff-James isomorphic simple $C^*$-algebras over the fields $\mathbb F_1$ and $\mathbb F_2$, respectively and if $\mathfrak A_1$ is finite-dimensional with dimension greater than one, then $\mathbb F_1=\mathbb F_2$ and $\mathfrak A_1$ and $\mathfrak A_2$ are (isometrically) $\ast$-isomorphic $C^*$-algebras.

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Bojan Kuzma, Sushil Singla. 2024-07-31. Non-linear classification of finite-dimensional simple $C^*$-algebras. https://arxiv.org/abs/2407.21582

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