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Irreducible unitary representation of non compact quantum group SUq(1,1) and its quantum symmetric space

非紧量子群SUq(1,1)及其量子对称空间的不可约酉表示

基本信息

批准号：
11440052
负责人：
MASUDA Tetsuya
金额：
$ 9.22万
依托单位：
University of Tsukuba
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (B)
财政年份：
1999
资助国家：
日本
起止时间：
1999 至 2002
项目状态：
已结题

项目摘要

The target of this research had been put in such a high level so that we were not able to carry out all the projects on the occasion that we asked for this research grant. On the process of our research concerning the quantum symmetric space, we recognized a quantum 4-dimensional spheres which are not realized as the quantum symmetric space, and we also succeeded to have an explicit construction of a quantum vector bundle on such spaces which are regarded to be very basic in the direction of quantum gauge theories leaving lots of problems to be studied in the future. Then, at the same time, we faced to compute the cyclic cohomologies of those quantum manifolds so that we decided to use a special type of computer system which had never tried to use for such a problem coming from pure mathematics due to the extremely huge amount of computations by hands. However, this problem of computer aided computation is still left together with the tunung of the computer system itself. On the other hand, a general framework to deal with the objects which are so called the locally compact quantum groups was eventually finished and already submitted to a journal in France. By making use of this framework, we are now ready to proceed in the direction of the very detailed study of the explicitly given examples of the quantum groups of the non compact type.

这项研究的目标被置于如此高的水平，以至于我们无法在我们要求这笔研究资助的情况下开展所有项目。在我们对量子对称空间的研究过程中，我们认识到了一个量子四维球面，但这类球面并不是量子对称空间，我们还成功地在这类空间上构造了一个量子向量丛，这在量子规范理论的方向上是非常基本的，还有许多问题有待于进一步的研究。然后，在同一时间，我们面临着计算这些量子流形的循环上同调，所以我们决定使用一种特殊类型的计算机系统，这种计算机系统从未尝试过用于这样一个来自纯数学的问题，因为手工计算量非常巨大。然而，这个计算机辅助计算的问题仍然与计算机系统本身的调试一起留下。另一方面，一个处理所谓的局部紧量子群的一般框架最终完成，并已提交给法国的一个期刊。通过利用这个框架，我们现在可以开始对明确给出的非紧型量子群的例子进行非常详细的研究了。