Categories of Symmetries and Infinite-Dimensional Groups

Erscheinungsjahr 1996
ISBN: 978-0-19-851186-1
Verlag: OUP Oxford

Buch, Englisch, 432 Seiten, Format (B × H): 161 mm x 240 mm, Gewicht: 816 g

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 book successfully 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 and graduate mathematicians.

Autoren/Hrsg.

Neretin, Yu A.

Weitere Mitwirkende

Gould, G. G.

Fachgebiete

• Mathematik | Informatik Mathematik Geometrie Algebraische Geometrie
• Mathematik | Informatik Mathematik Algebra Algebraische Strukturen, Gruppentheorie

Inhaltsverzeichnis

- Preface

- 1: Visible and invisible structures on infinite-dimensional groups

- 2: Spinor representation

- 3: Representations of the complex classical categories

- 4: Fermion Fock space

- 5: The Weil representation: finite-dimensional case

- 6: The Weil representation: infinite-dimensional case

- 7: Representations of the diffeomorphisms of a circle and the Virasoro algebra

- 8: The heavy groups

- 9: Infinite-dimensional classical groups and almost invariant structures

- 10: Some algebraic constructions of measure theory

- Appendix A The real classical categories

- Appendix B Semple complexes, hinges, and boundaries of symmetric spaces

- Appendix C Boson-fermion correspondence

- Appendix D Univalent functions and the Grunsky operator

- Appendix E Characteristic Livsic function

- Appendix F Examples, counterexamples, notes

- References

- Index