July 31, 2024Open Access

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

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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 A₁ and A₂ are Birkhoff-James isomorphic simple C^*-algebras over the fields F₁ and F₂, respectively and if A₁ is finite-dimensional with dimension greater than one, then F₁= F₂ and A₁ and A₂ are (isometrically) -isomorphic C^*-algebras.

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Kuzma et al. (Wed,) studied this question.

synapsesocial.com/papers/68e5e5bcb6db64358757a7aa https://doi.org/https://doi.org/10.48550/arxiv.2407.21582

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