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| Main Author: | |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2601.06950 |
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Table of Contents:
- Let $A$ be a unital locally matrix algebra. Among the examples of such algebras are: (1) an infinite tensor product $\otimes M_{n_i}(\mathbb{F})$ of matrix algebras over a field $\mathbb{F}$, and (2) the Clifford algebra of a nondegenerate quadratic form on an infinite-dimensional vector space over an algebraically closed field of characteristic different from $2$. We describe linear mappings $A \to B$ between unital locally matrix algebras that preserve the normalized rank. When $\mathbb{F}$ is a field of real or complex numbers, we also describe linear mappings $A \to A$ that preserve the normalized determinant.