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 Kahler manifolds and associated group actions which grew out of a DMVSeminar 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 BorelWeil 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, e.g., BorelWeil 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.
About A. Huckleberry
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Author  :  A. Huckleberry 
Publisher  :  Birkhauser Verlag AG 
Data Published  :  01 September 2001 
ISBN  :  3764366028 
EAN  :  9783764366025 
Format Book  :  PDF, Epub, DOCx, TXT 
Number of Pages  :  375 pages 
Age +  :  15 years 
Language  :  English 
Rating  : 
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