A study on pairings

配对研究

• 批准号: 04640111
• 负责人: ODA Nobuyuki
• 金额: $ 1.34万
• 依托单位: Fukuoka University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for General Scientific Research (C)
• 财政年份: 1992
• 资助国家: 日本
• 起止时间: 1992 至 1993
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-04640111/
• 关键词: pairing; category; translation plane; quatum group; pluriharmonic; dual connection; divergence; action; ホモトピー; ヒルベルト空間; 作用素; ホップ代数; 移行平面; 正則写像

We obtained some properties of pairings in general categories. We studied pairings concerning topologcal spaces, finite groups, quantum groups, pluriharmonic functions, differentiable manifolds, pseudo-Riemannian manifolds.We determined a class of translation planes of order q^3 admitting a collineation group of order q^3.For every Hopf **-algebra with a faithful Haar measure, we describe its regular representation as a direct sum of finite dimensional irreducible representations.Let EPSION be a DFN-space or a complex vector space with the finite open topology, (OMEGA, psi) be a Riemann domain over EPSILON and (lambda^^-, OMEGA^^-, psi^^-) the envelope of holomorphy of (OMEGA, psi). Then any real-valued pluriharmonic function on OMEGA is equal to the real part of a holomorphic function on OMEGA if and only if H^1(OMEGA^^-, R) = 0.We studied geometly of dual connections (metric-conjugate connections) on pseudo-Riemannian manifolds and he obtained the following result : When a dual connection has constant curvature, we can canonically determine a square-distance-like function which satisfies the generalized Pythagorean theorem.We consider finiteness obstructions of the total space for a principal fibration. If the fiber is a compact Lie group, we proved that there are many cases that the total space has an equivariant homotopy type of a finite equivariant CW complex under the restriction of the action.

我们在一般类别中获得了配对的一些属性。 We studied pairings concerning topologcal spaces, finite groups, quantum groups, pluriharmonic functions, differentiable manifolds, pseudo-Riemannian manifolds.We determined a class of translation planes of order q^3 admitting a collineation group of order q^3.For every Hopf **-algebra with a faithful Haar measure, we describe its regular representation as a direct sum of finite dimensional irreducible表示epsion是DFN空间或具有有限开放拓扑的复杂矢量空间，（Omega，psi）是Epsilon上的Riemann域，（lambda ^^ - ，Omega ^^ - ，PSI ^^ - ，PSI ^^ - ）（PSI ^^ - ）（OMEGA，PSI）的holomorphy的信封。那么，当且仅当且仅当H^1（Omega ^^ - ，r）= 0时，任何实现的欧米茄上的任何实值的Pluriharmonic功能都等于欧米茄上全体形态功能的实际部分平方距离的函数满足了广义的毕达哥拉斯定理。我们考虑主振动的总空间的有限障碍。如果纤维是一个紧凑的谎言组，我们证明了许多情况下，在限制下，总空间具有有限的eproivariant CW复合物的等效性同型类型。

项目成果

A.Inoue,H.Kurose,S.Ota: "Extensions of unbounded representation" Math.Nachr.155. 257-268 (1992)

A.Inoue、H.Kurose、S.Ota：“无界表示的扩展”Math.Nachr.155。

A.Inoue: "Partial O^*-algebras generated by two closed symmetric operators" J.Operator Theory.

A.Inoue：“由两个闭对称算子生成的部分 O^*-代数”J.算子理论。

K.Akiyama: "On the sherk plane" Journal of Geometory. (to appear).

K.Akiyama：“在谢克平面上”《几何杂志》。

T.Kanenobu & T.Sumi: "Polynomial invariants of 2-bridge knots through 22 crossings" Mathematics of Computations. vol.60. 771-778 (1993)

兼信

Y.Fukushima: "pluriharmonic functions as the real parts of holomorphic functions on a locally convex space" proceedings of the First Koren-Japanese Collo-quium on Finite or Infinite Dimensional Complex Analysis. 151-157 (1993)

Y.Fukushima：“复调和函数作为局部凸空间上全纯函数的实部”，第一届韩国-日本有限或无限维复分析学术讨论会的会议记录。