Categories of Symmetries and Infinite-Dimensional Groups

Hardcover | April 30, 1999

byYu A. NeretinTranslated byG. G. Gould

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For mathematicians working in group theory, the study of the many infinite-dimensional groups has been carried out in an individual and non-coherent way. For the first time, these apparently disparate groups have been placed together, in order to construct the `big picture'. This booksuccessfully gives an account of this - and shows how such seemingly dissimilar types such as the various groups of operators on Hilbert spaces, or current groups are shown to belong to a bigger entitity. This is a ground-breaking text will be important reading for advanced undergraduate andgraduate mathematicians.

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For mathematicians working in group theory, the study of the many infinite-dimensional groups has been carried out in an individual and non-coherent way. For the first time, these apparently disparate groups have been placed together, in order to construct the `big picture'. This booksuccessfully gives an account of this - and shows ...

Yu A. Neretin is at the Institute of Electronic Machine Building, Moscow, Bolshoi .
Format:HardcoverDimensions:432 pages, 9.21 × 6.14 × 1.1 inPublished:April 30, 1999Publisher:Oxford University Press

The following ISBNs are associated with this title:

ISBN - 10:0198511868

ISBN - 13:9780198511861

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Table of Contents

Preface1. Visible and invisible structures on infinite-dimensional groups2. Spinor representation3. Representations of the complex classical categories4. Fermion Fock space5. The Weil representation: finite-dimensional case6. The Weil representation: infinite-dimensional case7. Representations of the diffeomorphisms of a circle and the Virasoro algebra8. The heavy groups9. Infinite-dimensional classical groups and almost invariant structures10. Some algebraic constructions of measure theoryAppendix A The real classical categoriesAppendix B Semple complexes, hinges, and boundaries of symmetric spacesAppendix C Boson-fermion correspondenceAppendix D Univalent functions and the Grunsky operatorAppendix E Characteristic Livsic functionAppendix F Examples, counterexamples, notesReferencesIndex

Editorial Reviews

`The style of the book is clear. Ideas are well explained, and the author helps the readers to pass by several technical difficulties. The book can be recommended to researchers who are interested in symmetries and infinite-dimensional groups both from a theoretical and practical point ofview.'Zentrallblatt fur Mathematik und ihre Grenzgebiete No. 858, 1997