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arXiv 1003.0342math.QAmath-phmath.ACmath.MPmath.RAquant-ph
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量子平面上的无理Uq（sl2）对称性

Irrational Uq(sl2)-symmetries on the quantum plane

Steven Duplij, Sergey Sinel'shchikov

备注：
This paper was submitted to the arXiv as a concise preliminary version (without complete proofs and some additional material) of our preprint 0905.1719. Nevertheless, the removed preprint contained some material (e.g. classical limits and tables) which was absent in the full version 0905.1719. We decided to include this extra material to 0905.1719 and to withdraw the concise version
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摘要：

本文的主要结果是给出了量子平面的Uq（s1 ~ 2）-对称性的完整列表。为此，使用量子平面自同构的结构。我们对上述对称性进行分类的想法是引入一些特殊的符号矩阵来标记所讨论的一系列作用。这些矩阵描述了Uq（s1 ~ 2）的哪些生成元通过作用于量子平面的生成元而产生非零像。这些数据明确地确定了动作的权重。事实证明，有无数个同构类的对称。另一个结果是描述相应表示的合成列。给出了上述对称性的经典极限。

英文摘要：

The main result of this work is to present the complete list of Uq(sl2)-symmetries of quantum plane. For that, the structure of quantum plane automorphisms is used. Our idea in classifying the above symmetries is in introducing some special symbolic matrices to label the series of actions in question. The matrices depict which generators of Uq(sl2) produce nonzero images by acting on the generators of quantum plane. This data determines the weights of an action unambiguously. It turns out that there are uncountably many isomorphism classes of the symmetries. Another result is in describing composition series of the corresponding representations. The classical limit of the above symmetries is given.

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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