Published by De Gruyter 2014

Krichever–Novikov Type Algebras

Theory and Applications

Martin Schlichenmaier

Volume 53 in the series De Gruyter Studies in Mathematics

About this book

Krichever and Novikov introduced certain classes of infinite dimensional Lie algebras to extend the Virasoro algebra and its related algebras to Riemann surfaces of higher genus. The author of this book generalized and extended them to a more general setting needed by the applications. Examples of applications are Conformal Field Theory, Wess-Zumino-Novikov-Witten models, moduli space problems, integrable systems, Lax operator algebras, and deformation theory of Lie algebra. Furthermore they constitute an important class of infinite dimensional Lie algebras which due to their geometric origin are still manageable.

This book gives an introduction for the newcomer to this exciting field of ongoing research in mathematics and will be a valuable source of reference for the experienced researcher. Beside the basic constructions and results also applications are presented.

Author / Editor information

Martin Schlichenmaier, University of Luxembourg, Luxembourg.

Reviews

"[...] This is an interesting monograph and it will be useful both for experienced researchers and Ph.D. students working with infinite-dimensional Lie algebras, both on the mathematical side and on the side closer to theoretical physics."
Volodymyr Mazorchuk, Mathematical Reviews

"The book is excellent for studying the topic. [...] The book convinces the reader that – beside Krichever-Novikov type algebras being mathematically very interesting infinite dimensional geometric examples, – they are important in conformal field theory, integrable systems, deformations, and many other topics." Zentralblatt für Mathematik

Topics

Frontmatter Publicly Available Download PDF	i
Preface Requires Authentication Unlicensed Licensed Download PDF	v
Contents Publicly Available Download PDF	xi
1. Some background on Lie algebras Requires Authentication Unlicensed Licensed Download PDF	1
2. The higher genus algebras Requires Authentication Unlicensed Licensed Download PDF	8
3. The almost-grading Requires Authentication Unlicensed Licensed Download PDF	28
4. Fixing the basis elements Requires Authentication Unlicensed Licensed Download PDF	49
5. Explicit expressions for a system of generators Requires Authentication Unlicensed Licensed Download PDF	70
6. Central extensions of Krichever–Novikov type algebras Requires Authentication Unlicensed Licensed Download PDF	87
7. Semi-infinite wedge forms and fermionic Fock space representations Requires Authentication Unlicensed Licensed Download PDF	157
8. b − c systems Requires Authentication Unlicensed Licensed Download PDF	189
9. Affine algebras Requires Authentication Unlicensed Licensed Download PDF	212
10. The Sugawara construction Requires Authentication Unlicensed Licensed Download PDF	247
11. Wess–Zumino–Novikov–Witten models and Knizhnik–Zamolodchikov connection Requires Authentication Unlicensed Licensed Download PDF	275
12. Degenerations and deformations Requires Authentication Unlicensed Licensed Download PDF	303
13. Lax operator algebras Requires Authentication Unlicensed Licensed Download PDF	324
14. Some related developments Requires Authentication Unlicensed Licensed Download PDF	340
Bibliography Requires Authentication Unlicensed Licensed Download PDF	345
Index Requires Authentication Unlicensed Licensed Download PDF	357

(Deutsch)

Language: English
Publisher: De Gruyter
Audience: Graduate and PhD students, researchers in Lie algebras, algebraic geometry, mathematical physics; academic libraries.
Pages
- Front matter: 15
- Main content: 360
Keywords: Lie algebras; Riemann surfaces; Moduli spaces; Mathematical physics; Conformal field theory

eBook

Published: August 19, 2014
ISBN: 9783110279641

Hardcover

Published: July 28, 2014
ISBN: 9783110265170