Infinite dimensional Kähler manifolds
Infinite dimensional Kähler manifolds
复制标题
无限维凯勒流形
DOI：
10.1007/978-3-0348-8227-9
复制
发表时间：
2001
期刊：
影响因子：
0.7
通讯作者：
Tilmann Wurzbacher
中科院分区：
文献类型：
--
作者：
A. Huckleberry;Tilmann Wurzbacher
无穷维流形、李群和代数在数学和物理的许多领域中自然出现。已经被主要用作有限维对象的研究工具，重点已经改变，他们现在经常研究自己的独立利益。一方面，这是一个收集密切相关的文章无限维凯勒流形和相关的群体行动的增长出的DMV研讨会上同一主题。另一方面，它所涵盖的范围比上沃尔法赫研讨会期间可能涵盖的范围要大得多，在某种意义上，它是一种系统的方法，从该主题的基础到最近的事态发展。它应该对博士生和来自广泛领域的研究人员开放。最初的章节致力于一个相当独立的介绍群行动的复杂和辛流形和博雷尔-韦伊理论在有限维。接下来是无限维李群的基本处理，他们的行动和他们的代表。最后，一些更专业和先进的主题进行了讨论，例如，博雷尔-韦伊理论的循环群，方面的Virasoro代数，（规范）群行动和行列式丛，第二次量化和几何的无限维格拉斯曼流形。
Infinite dimensional manifolds, Lie groups and algebras arise naturally in many areas of mathematics and physics. Having been used mainly as a tool for the study of finite dimensional objects, the emphasis has changed and they are now frequently studied for their own independent interest. On the one hand this is a collection of closely related articles on infinite dimensional Kähler manifolds and associated group actions which grew out of a DMV-Seminar on the same subject. On the other hand it covers significantly more ground than was possible during the seminar in Oberwolfach and is in a certain sense intended as a systematic approach which ranges from the foundations of the subject to recent developments. It should be accessible to doctoral students and as well researchers coming from a wide range of areas. The initial chapters are devoted to a rather selfcontained introduction to group actions on complex and symplectic manifolds and to Borel-Weil theory in finite dimensions. These are followed by a treatment of the basics of infinite dimensional Lie groups, their actions and their representations. Finally, a number of more specialized and advanced topics are discussed, eg, Borel-Weil theory for loop groups, aspects of the Virasoro algebra,(gauge) group actions and determinant bundles, and second quantization and the geometry of the infinite dimensional Grassmann manifold.