某些量子行列式环中的素理想
Prime ideals in certain quantum determinantal rings
摘要：
研究了mxn矩阵的量子坐标代数A = Oq（PDMATHAMM（k））中2 × 2量子子式生成的理想I.证明了不变量理论第一和第二基本定理的类似定理。特别地，证明了I是完全素理想，即A/I是整环，A/I是k [x，x ^{-1}]在两个量子仿射空间的张量积Oq（k ^n）上的余作用的余不变量环. (That在作者的论文《量子行列式理想》中，证明了由txt量子子式生成的A的理想对任何t都是完全素的。存在由A上的（m + n）-环面作用诱导的A/I上的自然环面作用。我们确定了这个作用的不变素理想，并推导出A/I的素谱的结果。
英文摘要：
The ideal I generated by the 2x2 quantum minors in the algebra A = O_q(M_{m,n}(k)) (the quantized coordinate algebra of mxn matrices) is investigated. Analogues of the First and Second Fundamental Theorems of Invariant Theory are proved. In particular, it is shown that I is a completely prime ideal, that is, A/I is an integral domain, and that A/I is the ring of coinvariants of a coaction of k[x,x^{-1}] on O_q(k^m) tensor O_q(k^n), a tensor product of two quantum affine spaces. (That the ideal of A generated by the txt quantum minors, for any t, is completely prime is proved in the authors' paper `Quantum determinantal ideals'.) There is a natural torus action on A/I induced by an (m+n)-torus action on A. We identify the invariant prime ideals for this action and deduce consequences for the prime spectrum of A/I.
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