In this article, we define a set of matrices analogous to Vaserstein-type matrices, which were introduced in the paper ‘Serre's problem on projective modules over polynomial rings and algebraic K-theory’ by Suslin–Vaserstein in 1976. We prove that these are elementary linear matrices. Also, under some conditions, these matrices belong to Petrov's odd unitary group, which is a generalization of all classical groups. We also prove that these matrices generate the Petrov's odd elementary hyperbolic unitary group when the ring is commutative.

中文翻译：

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彼得罗夫奇酉群的可视化

在本文中，我们定义了一组类似于 Vaserstein 型矩阵的矩阵，这些矩阵在 Suslin-Vaserstein 在 1976 年的论文“Serre's problem on projective modules over polynomial ring and algebraic K -theory”中被介绍。我们证明这些是初等线性矩阵。此外，在某些条件下，这些矩阵属于彼得罗夫奇酉群，它是所有经典群的推广。我们还证明了当环是可交换的时，这些矩阵生成了 Petrov 的奇初等双曲酉群。