Differential Geometry, Lie Groups and Symmetric Spaces over. General Base Fields and Rings

Wolfgang Bertram

首页> 外文期刊>Memoirs of the American Mathematical Society >Differential Geometry, Lie Groups and Symmetric Spaces over. General Base Fields and Rings

【24h】

Differential Geometry, Lie Groups and Symmetric Spaces over. General Base Fields and Rings

机译：微分几何，李群和对称空间。通用基础字段和环

获取原文

掌桥外文数据库（机构版） >>

开具论文收录证明 >>

文献代查 >>

页面导航

摘要
著录项
相似文献
相关主题

摘要

The aim of this work is to lay the foundations of differential geometry and Lie theory over the general class of topological base fields and -rings for which a differential calculus has been developed in [BGN04], without any restriction on the dimension or on the characteristic. Two basic features distinguish our approach from the classical real (finite or infinite dimensional) theory, namely the interpretation of tangent- and jet functors as functors of scalar extensions and the introduction of multilinear bundles and multilinear connections which generalize the concept of vector bundles and linear connections.

机译：这项工作的目的是为[BGN04]中已经开发出微积分的拓扑基类和环的一般类别奠定微分几何和李理论的基础，而对尺寸或特性没有任何限制。我们的方法有两个基本特征与经典的实（有限或无限维）理论不同，即将切线和射流函子解释为标量扩展函子，以及引入了多线性束和多线性连接，这些向量笼统地概括了矢量束和线性连接。

著录项

来源
《Memoirs of the American Mathematical Society》 |2008年第900期|共199页
作者
Wolfgang Bertram;
展开▼
作者单位

展开▼
收录信息
原文格式 PDF
正文语种 eng
中图分类数学;
关键词
Lie groups over topological fields; infinite-dimensional Lie groups; diffeomorphism groups; formal group; general and special multilinear group; symmetric space; differentiable manifold; tangent functor; linear and multilinear bundle; jet; linear connection; multilinear connection; curvature; exponential map; exponentialjet; Campbell-Hausdorff formula; multilinear algebra; scalar extension; dual numbers; synthetic differential geometry; Weil functor;

机译：拓扑领域上的李群;无穷维李群;亚同性群;形式群;一般和特殊多线性群;对称空间;可分流形;切函子;线性和多线性束;射流;线性连接;多线性连接;曲率;指数图指数射流;Campbell-Hausdorff公式;多线性代数;标量扩展;对数;合成微分几何;Weil仿函数;

相似文献

外文文献
中文文献
专利

1. Differential Geometry, Lie Groups and Symmetric Spaces over. General Base Fields and Rings [J] . Wolfgang Bertram Memoirs of the American Mathematical Society . 2008,第900期

机译：微分几何，李群和对称空间。通用基础字段和环
2. Symmetric spaces and Lie triple systems in numerical analysis of differential equations [J] . H. Z. Munthe-Kaas, G. R. W. Quispel, A. Zanna BIT numerical mathematics . 2014,第1期

机译：微分方程数值分析中的对称空间和李三重系统
3. Paley-Wiener theorems and surjectivity of invariant differential operators on symmetric spaces and Lie groups [J] . Helgason Sigurdur Bulletin of the American Mathematical Society . 1973,第1期

机译：对称空间和李群上不变微分算子的Paley-Wiener定理和排斥性
4. Surrouding structures analysis of pulmonay nodules using differential geometry based vector fields [C] . Kawata, Y., Niki, Image Processing, 2000. Proceedings. 2000 International Conference on . 2000

机译：基于微分几何矢量场的肺结节周围结构分析
5. TOTAL FOLIATIONS ON 3-MANIFOLDS AND THE GEOMETRY OF SPACES OF COFRAMEFIELDS (TOPOLOGY, DIFFERENTIAL). [D] . MENN, STEPHEN. 1985

机译：3流形上的总叶片数和共形空间的几何形状（拓扑，微分）。
6. Fringe Phase-Shifting Field Based Fuzzy Quotient Space-Oriented Partial Differential Equations Filtering Method for Gaussian Noise-Induced Phase Error [O] . Changzhi Yu, Fang Ji, Junpeng Xue, 2019

机译：基于边缘相移场的高斯噪声相位误差的模糊商空间偏微分方程滤波方法
7. Differential geometry, Lie groups and symmetric spaces over general base fields and rings [O] . Wolfgang Bertram, Cartan U. M. R 2012

机译：一般基本场和环上的微分几何，李群和对称空间

Differential Geometry, Lie Groups and Symmetric Spaces over. General Base Fields and Rings

摘要

著录项

相似文献

相关主题

期刊订阅