Infinite Dimensional Representation, Measure Theory and Related Topics
无限维表示、测度论及相关主题
基本信息
- 批准号:09640171
- 负责人:
- 金额:$ 0.51万
- 依托单位:
- 依托单位国家:日本
- 项目类别:Grant-in-Aid for Scientific Research (C)
- 财政年份:1997
- 资助国家:日本
- 起止时间:1997 至 1998
- 项目状态:已结题
- 来源:
- 关键词:
项目摘要
Between these two years I contained to study on unitary representations of the group of. diffeomorphisms with compact support Diff_0(M) or of its subgroups on smooth manifolds M.It is known that these groups are infinite dimensional Lie groups, whenever M is compact. Hence there is possibility to analyze these representations with the Lie algebraic method. Under these considerations I have obtained the following results for reducibility our unitary representations to the linear one.1 The linearlity is assured by a formula which corresponds to the Campbell-Hausdorff formula on the usual Lie group. (In our case, the formula comes from an evaluation for the behavior of solutions of some autonomus differential equations)2. A chracterization of the subgroup generated by the image of Lie algebra by the exponential mapping.For the above problem I have seen that it is no problem to proceed our theories, for example in the case of Diff_0(M), the subgroup is dense in the connected component of the neutral element.3. Lastly, for the problem of rich existence of C^*-vectors I am continuing to discuss it now, of course on infinite dimensional representations.Moreover I applied the above results to 1-cocycles in terms of Diff_0(M) and obtained some fundamental results. In particular the cocycle form has a close connection with the geometrical structure on M.
在这两年中,我开始研究群的酉表示。光滑流形M上紧支持Diff_0(M)或其子群的微分同态,已知当M紧时,这些群是无穷维李群。因此,有可能用李代数方法来分析这些表示。在这些考虑下,我得到了以下结果,可以将我们的幺正表示约化为线性表示线性性由一个公式来保证,该公式与一般李群上的Campbell-Hausdorff公式相对应。(在我们的例子中,这个公式来自于对一些自主微分方程解的行为的评估)用指数映射刻画李代数象所产生的子群。对于上述问题,我已经看到,继续我们的理论是没有问题的,例如在Diff_0(M)的情况下,子群在中性元素的连通分量中是密集的。最后,对于C^*向量的丰富存在性问题,我现在继续讨论它,当然是在无限维表示上。并将上述结果应用到关于Diff_0(M)的1环上,得到了一些基本结果。特别是循环形式与M上的几何结构有密切的联系。
项目成果
期刊论文数量(8)
专著数量(0)
科研奖励数量(0)
会议论文数量(0)
专利数量(0)
H.Shimomura: "Unitary representations and 1-cocycles on the group of diffeomorphisms" RIMS.kokyuroku. (近刊).
H.Shimomura:“微分同胚群上的幺正表示和 1-余循环”RIMS.kokyuroku(即将出版)。
- DOI:
- 发表时间:
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- 影响因子:0
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- 通讯作者:
H.Shimomura: "Relations between unitary representations of diffeomorphism groups and those of the infinite symmetric group or related permutation groups (with T.Hirai)" J.Math.Kyoto Uinv.37. 261-316 (1997)
H.Shimomura:“微分同胚群的酉表示与无限对称群或相关排列群(与 T.Hirai)的酉表示之间的关系”J.Math.Kyoto Uinv.37。
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- 影响因子:0
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H.SHIMOMURA: "CANONICAL Representations Generated by translctconally quesi-inva" riant measnres,PUBL.RIMS.Kyoto Univ.32.No4. 633-669 (1996)
H.SHIMOMURA:“由 translctconally quesi-inva 生成的规范表示”riant measnres,PUBL.RIMS.Kyoto Univ.32.No4。
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- 影响因子:0
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- 通讯作者:
下村 宏彰: "1-cocycles on infinite dimensional spaces" 数理解析研究所講究録. 1017. 116-123 (1997)
Hiroaki Shimomura:“无限维空间上的 1-cocycles”数学分析研究所的 Kokyuroku。1017. 116-123 (1997)
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- 影响因子:0
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- 通讯作者:
H.Shimomura: "1-cocycles on the group of diffeomorphisms." J.Math.Kyoto Univ.38(in press).
H.Shimomura:“微分同胚群上的 1-余循环。”
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SHIMOMURA Hiroaki其他文献
SHIMOMURA Hiroaki的其他文献
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{{ truncateString('SHIMOMURA Hiroaki', 18)}}的其他基金
Representation and measure theory of infinite dimensional moues and its applications
无限维运动的表示与测度理论及其应用
- 批准号:
18540184 - 财政年份:2006
- 资助金额:
$ 0.51万 - 项目类别:
Grant-in-Aid for Scientific Research (C)
Representation theory and measure theory of infinite-dimensional groups and related topics
无限维群的表示论和测度论及相关话题
- 批准号:
16540162 - 财政年份:2004
- 资助金额:
$ 0.51万 - 项目类别:
Grant-in-Aid for Scientific Research (C)
Infinite Dimensional Representations and Related Topics
无限维表示及相关主题
- 批准号:
14540167 - 财政年份:2002
- 资助金额:
$ 0.51万 - 项目类别:
Grant-in-Aid for Scientific Research (C)
Infinite Dimensional Representations and Related Topics
无限维表示及相关主题
- 批准号:
12640164 - 财政年份:2000
- 资助金额:
$ 0.51万 - 项目类别:
Grant-in-Aid for Scientific Research (C)