$K_1$-Stability of symplectic modules over monoid algebras
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866918001908908032 |
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| author | Basu, Rabeya Mathew, Maria Ann |
| author_facet | Basu, Rabeya Mathew, Maria Ann |
| contents | Let $R$ be a regular ring of dimension $d$ and $L$ be a $c$-divisible monoid. If ${K}_1{Sp}(R)$ is trivial and $k \geq d+2,$ then we prove that the symplectic group ${Sp}_{2k}(R[L])$ is generated by elementary symplectic matrices over $R[L]$. When $d \leq 1$ or $R$ is a geometrically regular ring containing a field, then improved bounds have been established. We also discuss the linear case, extending the work of Gubeladze. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2504_19492 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | $K_1$-Stability of symplectic modules over monoid algebras Basu, Rabeya Mathew, Maria Ann Commutative Algebra K-Theory and Homology Rings and Algebras Let $R$ be a regular ring of dimension $d$ and $L$ be a $c$-divisible monoid. If ${K}_1{Sp}(R)$ is trivial and $k \geq d+2,$ then we prove that the symplectic group ${Sp}_{2k}(R[L])$ is generated by elementary symplectic matrices over $R[L]$. When $d \leq 1$ or $R$ is a geometrically regular ring containing a field, then improved bounds have been established. We also discuss the linear case, extending the work of Gubeladze. |
| title | $K_1$-Stability of symplectic modules over monoid algebras |
| topic | Commutative Algebra K-Theory and Homology Rings and Algebras |
| url | https://arxiv.org/abs/2504.19492 |