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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2410.07631 |
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| _version_ | 1866910643803652096 |
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| author | Basu, Rabeya Mathew, Maria Ann |
| author_facet | Basu, Rabeya Mathew, Maria Ann |
| contents | The elementary action of symplectic and orthogonal groups on unimodular rows of length $2n$ is transitive for $2n \geq \max(4, d+2)$ in the symplectic case, and $2n \geq \max(6, 2d+4)$ in the orthogonal case, over monoid rings $R[M]$, where $R$ is a commutative noetherian ring of dimension $d$, and $M$ is commutative cancellative torsion free monoid. As a consequence, one gets the surjective stabilization bound for the $K_1$ for classical groups. This is an extension of J. Gubeladze's results for linear groups. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_07631 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Elementary Action of Classical Groups on Unimodular Rows Over Monoid Rings Basu, Rabeya Mathew, Maria Ann Commutative Algebra K-Theory and Homology Rings and Algebras 11E57, 11E70, 13-02, 15A63, 19A13, 19B14, 20M25 The elementary action of symplectic and orthogonal groups on unimodular rows of length $2n$ is transitive for $2n \geq \max(4, d+2)$ in the symplectic case, and $2n \geq \max(6, 2d+4)$ in the orthogonal case, over monoid rings $R[M]$, where $R$ is a commutative noetherian ring of dimension $d$, and $M$ is commutative cancellative torsion free monoid. As a consequence, one gets the surjective stabilization bound for the $K_1$ for classical groups. This is an extension of J. Gubeladze's results for linear groups. |
| title | Elementary Action of Classical Groups on Unimodular Rows Over Monoid Rings |
| topic | Commutative Algebra K-Theory and Homology Rings and Algebras 11E57, 11E70, 13-02, 15A63, 19A13, 19B14, 20M25 |
| url | https://arxiv.org/abs/2410.07631 |