Rank metric isometries and determinant-preserving mappings on II$_1$-factors
Operator Algebras
2025-06-16 v1
Abstract
We fully describe the general form of a linear (or conjugate-linear) rank metric isometry on the Murray--von Neumann algebra associated with a II-factor. As an application, we establish Frobenius' theorem in the setting of II-factors, by showing that every determinant-preserving linear bijection between two II-factors is necessarily an isomorphism or an anti-isomorphism. This confirms the Harris--Kadison conjecture (1996).
Keywords
Cite
@article{arxiv.2506.11428,
title = {Rank metric isometries and determinant-preserving mappings on II$_1$-factors},
author = {Jinghao Huang and Karimbergen Kudaybergenov and Fedor Sukochev},
journal= {arXiv preprint arXiv:2506.11428},
year = {2025}
}