量子$3\times3$矩阵的缠绕不变素理想
Winding-invariant prime ideals in quantum $3\times3$ matrices
摘要：
给出了一般3 × 3量子矩阵代数中缠绕自同构下的素理想不变量的一个完全判定。对于所有这些素数，给出了由量子子式组成的显式生成集，从而验证了3 × 3情形下的一个一般猜想。结果严重依赖于某些张量积分解的缠绕不变的素理想，在一个附带的文件。此外，新的方法在这里开发，这表明，某些套量子子，以前无法管理，产生素理想的n × n量子矩阵代数。
英文摘要：
A complete determination of the prime ideals invariant under winding automorphisms in the generic 3 by 3 quantum matrix algebra is obtained. Explicit generating sets consisting of quantum minors are given for all of these primes, thus verifying a general conjecture in the 3 by 3 case. The result relies heavily on certain tensor product decompositions for winding-invariant prime ideals, developed in an accompanying paper. In addition, new methods are developed here, which show that certain sets of quantum minors, not previously manageable, generate prime ideals in the n by n quantum matrix algebra.
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