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.

我们获得了一般类别中配对的一些属性。我们研究了有关拓扑空间、有限群、量子群、复调和函数、可微流形、伪黎曼流形的配对。我们确定了一类 q^3 阶的平移平面，允许 q^3 阶的直射群。对于每个 Hopf * *-具有忠实 Haar 测度的代数，我们将其正则表示描述为有限维不可约表示的直和。设 EPSION 为 DFN 空间或复向量空间对于有限开放拓扑，(OMEGA, psi) 是 EPSILON 上的黎曼域，(lambda^^-, OMEGA^^-, psi^^-) 是 (OMEGA, psi) 的全纯包络。那么 OMEGA 上的任何实值多调和函数都等于 OMEGA 上全纯函数的实部当且仅当 H^1(OMEGA^^-, R) = 0。我们研究了对偶连接（度量共轭连接）的几何）在伪黎曼流形上，他得到了以下结果：当对偶连接具有恒定曲率时，我们可以规范地确定满足广义平方距离的函数毕达哥拉斯定理。我们考虑主纤维振动的总空间的有限性障碍。如果纤维是紧李群，我们证明了在很多情况下，总空间在作用的限制下具有有限等变CW复形的等变同伦型。

项目成果

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。

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。

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

K.Akiyama: "On the Sherk Plane" Journal of Geometry(to appear).

K.Akiyama：“On the Sherk Plane”《几何杂志》（即将出版）。