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September 10, 2025Open Access

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

Key Points

Finite-dimensional simple C*-algebras are characterized by their underlying Banach space structures.
If two C*-algebras A1 and A2 are isomorphic, their underlying fields must also be the same.
Non-linear classification methods provide deeper insights into the structure of C*-algebras.
The results have implications for understanding algebraic properties in a finite-dimensional setting.

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 is omorphic 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.

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

Key Points

Abstract

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