Normalized Rank- and Determinant-Preserving Mappings of Locally Matrix Algebras
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arXiv
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866909987429679104 |
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| author | Bezushchak, Oksana |
| author_facet | Bezushchak, Oksana |
| 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_06950 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Normalized Rank- and Determinant-Preserving Mappings of Locally Matrix Algebras Bezushchak, Oksana Rings and Algebras 15A15, 15A86, 47B49 (Primary) 15A30, 15A66, 16W10 (Secondary) 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. |
| title | Normalized Rank- and Determinant-Preserving Mappings of Locally Matrix Algebras |
| topic | Rings and Algebras 15A15, 15A86, 47B49 (Primary) 15A30, 15A66, 16W10 (Secondary) |
| url | https://arxiv.org/abs/2601.06950 |