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arXiv 1312.4682math.QA
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对于量子化Picard-Vessiot理论,对我们前面例子的进一步观察

Toward quantized Picard-Vessiot theory, Further observations on our previous example

Katsunori Saito, Hiroshi Umemura

摘要:

人们很自然地想知道是否存在一个差分微分方程,它的伽罗瓦群是一个既不是交换的也不是余交换的量子群。我们相信不存在这样的线性方程,于是探索非线性方程,发现了这样一个方程。我们证明了这个例子与一个线性方程有关。我们只讨论一个迷人的例子。然而,这不是一个孤立的例子。我们打开一个窗口,让我们看看量子化的Picard-Vessiot理论。

英文摘要:

It is quite natural to wonder whether there is a difference-differential equations, the Galois group of which is a quantum group that is neither commutative nor co-commutative. Believing that there was no such linear equations, we explored non-linear equations and discovered a such equation. We show that the example is related with a linear equation. We treat only one charming example. It is not, however, an isolated example. We open a window that allows us to have a look at a quantized Picard-Vessiot theory.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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