Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2026
|
| Schlagworte: | |
| Online-Zugang: | https://arxiv.org/abs/2601.11059 |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866908769732001792 |
|---|---|
| author | Choudhury, Projesh Nath Fallat, Shaun Li, Chi-Kwong |
| author_facet | Choudhury, Projesh Nath Fallat, Shaun Li, Chi-Kwong |
| contents | Totally positive (TP) and totally nonnegative (TN) matrices connect to analysis, mechanics, and to dual canonical bases in reductive groups, by well-known works of Schoenberg, Gantmacher-Krein, Lusztig, and others. TP matrices form a multiplicatively closed semigroup, contained in the larger monoid of invertible totally nonnegative (ITN) matrices. Whitney and Berenstein-Fomin-Zelevinsky found bidiagonal factorizations of all $n\times n$ ITN and TP matrices into multiplicative generators; a natural question now is to classify the multiplicative automorphisms of these semigroups. In this article, we classify all automorphisms of these semigroups of ITN and TP matrices. In particular, we show that the automorphisms are the same, and they respect the multiplicative generators. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_11059 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Semigroup automorphisms of total positivity Choudhury, Projesh Nath Fallat, Shaun Li, Chi-Kwong Rings and Algebras Totally positive (TP) and totally nonnegative (TN) matrices connect to analysis, mechanics, and to dual canonical bases in reductive groups, by well-known works of Schoenberg, Gantmacher-Krein, Lusztig, and others. TP matrices form a multiplicatively closed semigroup, contained in the larger monoid of invertible totally nonnegative (ITN) matrices. Whitney and Berenstein-Fomin-Zelevinsky found bidiagonal factorizations of all $n\times n$ ITN and TP matrices into multiplicative generators; a natural question now is to classify the multiplicative automorphisms of these semigroups. In this article, we classify all automorphisms of these semigroups of ITN and TP matrices. In particular, we show that the automorphisms are the same, and they respect the multiplicative generators. |
| title | Semigroup automorphisms of total positivity |
| topic | Rings and Algebras |
| url | https://arxiv.org/abs/2601.11059 |