二元域上正交群的不变环
Invariant rings of orthogonal groups over the field of two elements
摘要：
对于V上保持非奇异二次型的正交变换群G，我们在二元域上的向量空间V的对偶上确定了对称代数中的不变量环。它被证明是一个完整的交叉点。特别是，这里计算的不变量环都是Gorenstein，因此是Cohen-Macaulay。
英文摘要：
We determine the rings of invariants in the symmetric algebra on the dual of a vector space V over the field of two elements, for the group G of orthogonal transformations preserving a non-singular quadratic form on V. The invariant ring is shown to have a presentation in which the difference between the number of generators and the number of relations is equal to the minimum possibility, namely the dimension of V, and it is shown to be a complete intersection. In particular, the rings of invariants computed here are all Gorenstein and hence Cohen-Macaulay.
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