Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2511.12282 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866912712079966208 |
|---|---|
| author | Ogievetsky, Oleg Pyatov, Pavel |
| author_facet | Ogievetsky, Oleg Pyatov, Pavel |
| contents | For a family of the orthogonal $O(k)$ type Quantum Matrix algebras we establish an analogue of the Cayley--Hamilton theorem. The form of the Cayley-Hamilton identity is different in three cases. First, the cases of odd ($k=2\ell -1$) and even ($k=2\ell$) heights are different. Second, for even height orthogonal Quantum Matrix algebra we derive two versions of the Cayley--Hamilton theorem, one for its positive component $O^+(2\ell)$ and another one for the negative component $O^-(2\ell)$. In each case we introduce the spectral parameterization of the coefficients of the Cayley--Hamilton identity by the `eigenvalues' of the quantum matrices. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_12282 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Cayley--Hamilton Theorem for Orthogonal Quantum Matrix Algebras Ogievetsky, Oleg Pyatov, Pavel Quantum Algebra Mathematical Physics Rings and Algebras 20G42, 16S37 For a family of the orthogonal $O(k)$ type Quantum Matrix algebras we establish an analogue of the Cayley--Hamilton theorem. The form of the Cayley-Hamilton identity is different in three cases. First, the cases of odd ($k=2\ell -1$) and even ($k=2\ell$) heights are different. Second, for even height orthogonal Quantum Matrix algebra we derive two versions of the Cayley--Hamilton theorem, one for its positive component $O^+(2\ell)$ and another one for the negative component $O^-(2\ell)$. In each case we introduce the spectral parameterization of the coefficients of the Cayley--Hamilton identity by the `eigenvalues' of the quantum matrices. |
| title | Cayley--Hamilton Theorem for Orthogonal Quantum Matrix Algebras |
| topic | Quantum Algebra Mathematical Physics Rings and Algebras 20G42, 16S37 |
| url | https://arxiv.org/abs/2511.12282 |