Noncommutative Poisson structure and invariants of matrices
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866916123206746112 |
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| author | Eshmatov, Farkhod García-Martínez, Xabier Turdibaev, Rustam |
| author_facet | Eshmatov, Farkhod García-Martínez, Xabier Turdibaev, Rustam |
| contents | We introduce a novel approach that employs techniques from noncommutative Poisson geometry to comprehend the algebra of invariants of two $n\times n$ matrices. We entirely solve the open problem of computing the algebra of invariants of two $4 \times 4$ matrices. As an application, we derive the complete description of the invariant commuting variety of $4 \times 4$ matrices and the fourth Calogero-Moser space. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_06909 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Noncommutative Poisson structure and invariants of matrices Eshmatov, Farkhod García-Martínez, Xabier Turdibaev, Rustam Rings and Algebras 16R30, 16S38, 14A22, 13A50 We introduce a novel approach that employs techniques from noncommutative Poisson geometry to comprehend the algebra of invariants of two $n\times n$ matrices. We entirely solve the open problem of computing the algebra of invariants of two $4 \times 4$ matrices. As an application, we derive the complete description of the invariant commuting variety of $4 \times 4$ matrices and the fourth Calogero-Moser space. |
| title | Noncommutative Poisson structure and invariants of matrices |
| topic | Rings and Algebras 16R30, 16S38, 14A22, 13A50 |
| url | https://arxiv.org/abs/2402.06909 |