量子“az+b”群的指数方程
Exponential equations for the quantum "az+b" group
摘要：
在希尔伯特空间水平上考虑量子群理论。我们发现所有的解决方案的标量和一般指数方程的量子“az+ b”组。结果表明，所有涉及量子指数函数F_N的方程都有一个简单的公式。我们顺便证明了一个非常有趣的定理，即关于某些正规算子和的正规扩张的存在性定理。换句话说，我们找到了与量子"az+ b“群相关的辫状量子群的所有酉表示。这是对量子"az+ b“群的所有酉表示进行分类所需的最困难的结果。最终，这使我们能够在下一篇论文中给出量子"ax+ b“群的所有酉表示的公式。
英文摘要：
We consider quantum group theory on the Hilbert space level. We find all solutions for scalar and general exponential equations for the quantum ``az+b'' group. It turns out that there is a simple formula for all of them involving the quantum exponential function F_N. The very interesting theorem we prove by the way is the one on the existence of normal extension of certain sum of normal operators. To put it differently, we find all unitary representations of the braided quantum group related to the quantum ``az+b'' group. This is the most difficult result needed to classify all unitary representations of the quantum ``az+b'' group. Eventually this enables us to give a formula for all unitary representations of the quantum ``ax+b'' group in our next paper.
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