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<p>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 generalize the result of Kopeiko for a symplectic group defined with respect to any invertible skew-symmetric matrix of Pfaffian one. We also establish this equality over a semi-local ring.</p>

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Equality of elementary symplectic group and symplectic group

  • 期刊论文

  • 发表日期：

    2026年7月30日

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  • Ruddarraju Amrutha,
  • Pratyusha Chattopadhyay

摘要

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 generalize the result of Kopeiko for a symplectic group defined with respect to any invertible skew-symmetric matrix of Pfaffian one. We also establish this equality over a semi-local ring.