Equality of elementary symplectic group and symplectic group
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866915063695147008 |
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| author | Amrutha, Ruddarraju Chattopadhyay, Pratyusha |
| author_facet | Amrutha, Ruddarraju Chattopadhyay, Pratyusha |
| contents | V.I. Kopeiko proved that over a euclidean ring, the symplectic group defined with respect to the standard skew-symmetric matrix is same as the elementary symplectic group. Here we generalise the result of Kopeiko for a symplectic group defined with respect to any invertible skew-symmetric matrix of Pfaffian one. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_10696 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Equality of elementary symplectic group and symplectic group Amrutha, Ruddarraju Chattopadhyay, Pratyusha Commutative Algebra 13A99, 15A24, 15A54, 15B99, 20H25 V.I. Kopeiko proved that over a euclidean ring, the symplectic group defined with respect to the standard skew-symmetric matrix is same as the elementary symplectic group. Here we generalise the result of Kopeiko for a symplectic group defined with respect to any invertible skew-symmetric matrix of Pfaffian one. |
| title | Equality of elementary symplectic group and symplectic group |
| topic | Commutative Algebra 13A99, 15A24, 15A54, 15B99, 20H25 |
| url | https://arxiv.org/abs/2412.10696 |