多项式环上正交矩阵的有界约化
Bounded reduction of orthogonal matrices over polynomial rings
摘要：
证明了系数在小维环上的多项式环上的分裂正交群的矩阵可以通过有限个初等正交变换化为更小的矩阵.界限是明确给出的。这个结果是Suslin和Kopeiko证明的正交K1函子的早期稳定性的有效版本。由于Vaserstein对特殊的线性群和辛群得到了类似的有效结果，本文封闭了分裂典型群的问题.
英文摘要：
We prove that a matrix from the split orthogonal group over a polynomial ring with coefficients in a small-dimensional ring can be reduced to a smaller matrix by a bounded number of elementary orthogonal transformations. The bound is given explicitly. This result is an effective version of the early stabilisation of the orthogonal K1 functor proven by Suslin and Kopeiko. Since the similar effective results for special linear and symplectic groups were obtained by Vaserstein, the present paper closes the problem for split classical groups.
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