Reseach of non commutative geometry

非交换几何研究

• 批准号: 14540092
• 负责人: OMORI Hideki
• 金额: $ 2.11万
• 依托单位: TOKYO UNIVERSITY OF SCIENCE
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2002
• 资助国家: 日本
• 起止时间: 2002 至 2004
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-14540092/
• 关键词: Non-commutative Geometry; Star-product; Deformation quantization; *-積; 量子化

In the transcendently extended Weyl algebra, there was no systematic theory of intertwiners. This research attempt to construct a systematic theory for these. Here is the summary of facts, uncovered by the research :1)Existence of multi-valued elementsThis is observed as monodromy phenomena for the parallel translation by infinitesimal intertwiners. That is, even though the parameter of expression came back to the starting point, the parallelly translated element did not come back to the starting point.2)Group-like object which does not form a point setThis is viewd as a model regarded as a non-trivial double covering group of a "simply connected" Lie group.In the traditional mathematics, such an object is logically impossible. However, it is permitted to exist, because of the existence of multi-valued elements.3)Manifolds patched by multi-valued coordinate transformationsMulti-valued functions are familiar in classical mathematics. However, there was no notion of manifolds, which are understood as a patchwork of local coordnate neighborhoods by multivalued coordinate transformations. Such notions are required to understand the phenomena mentioned above.

在超级扩展的Weyl代数中，没有互换的系统理论。这项研究试图为这些构建系统理论。这是事实的摘要，从研究中发现：1）存在多价元素的存在，这些元素被视为无限小型互穿的平行翻译的单片现象。也就是说，即使表达式的参数又回到了起点，也没有回到起点。2）类似群的对象，该对象不形成一个点，这是一个被视为被视为一个模型一个“简单连接”的谎言组的非平凡的双重覆盖组。在传统数学中，这种对象在逻辑上是不可能的。但是，由于存在多值元素，因此可以存在。3）在经典数学中熟悉了由多价值坐标变换函数修补的歧管。但是，没有流形的概念，这些概念被多相坐标转换理解为局部坐标社区的拼布。需要这样的概念来了解上述现象。

项目成果

数学の中の物理学

数学中的物理

• 发表时间: 2004
• 作者: H.Omori;Y.Maeda;N.Miyazaki;A.Yoshioka;大森英樹
• 通讯作者: 大森英樹

Star exponential functions for quadratic forms and polar elements

二次型和极元的星指数函数

• 发表时间: 2002
• 期刊: Contem.Math.A.M.S. 315
• 作者: H.Omori;Y.Maeda;N.Miyazaki;A.Yoshioka
• 通讯作者: A.Yoshioka

Associativity breaks down in deformation quantization

变形量化中关联性失效

• 发表时间: 2003
• 期刊: Advanced Studies in Pure Math. 37
• 作者: Hisao Kato;Eiichi;Matsuhashi;加藤久男;H.Omori
• 通讯作者: H.Omori

Star exponeutial functions for quadratic forms and polar elements

二次形式和极元的星型指数函数

• 发表时间: 2002
• 期刊: Contem.Math.A.M.S. 315
• 作者: H.Omori;Y.Maeda.N.Miyazaki;A.Yoshioka
• 通讯作者: A.Yoshioka

Hideki Omori: "One must break symmetry in order to keep associativity"Banach center publications. 55. 153-163 (2002)

大森英树：“必须打破对称性才能保持结合性”巴拿赫中心出版物。