Krichever-Novikov Type Algebras : Theory and Applications

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. In this title, the author generalized and extended them to a more general setting needed by the applications.

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.

"[...] 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