{"product_id":"infinite-dimensional-kahler-manifolds-9783764366025","title":"Infinite Dimensional Kähler Manifolds","description":"\u003cp\u003e • Author(s): Alan Huckleberry\u003cbr\u003e • Publisher: Springer\u003cbr\u003e • Publisher Imprint: Birkhauser\u003cbr\u003e • BISAC: Geometry - Differential\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003eInfinite 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, e.g., 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.\u003c\/p\u003e","brand":"Springer","offers":[{"title":"Paperback","offer_id":45283930996887,"sku":"9783764366025","price":3672.0,"currency_code":"INR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0666\/3471\/1191\/files\/9783764366025.webp?v=1769279666","url":"https:\/\/atlanticbooks.com\/products\/infinite-dimensional-kahler-manifolds-9783764366025","provider":"Atlantic Books","version":"1.0","type":"link"}