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This is the third, substantially revised edition of this important monograph. The book is concerned with Kac-Moody algebras, a particular class of infinite-dimensional Lie algebras, and their representations. It is based on courses given over a number of years at MIT and in Paris, and is sufficiently self-contained and detailed to be used for graduate courses. Each chapter begins with a motivating discussion and ends with a collection of exercises, with hints to the more challenging problems.
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Infinite dimensional Lie algebras --- 512.81 --- Lie groups --- Infinite dimensional Lie algebras. --- 512.81 Lie groups --- Lie, Algèbres de
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Ordered algebraic structures --- Lie algebras --- Algèbres de Lie --- 512 --- Infinite dimensional Lie algebras --- Algebra --- Infinite dimensional Lie algebras. --- 512 Algebra --- Algèbres de Lie --- Lie, Algèbres de
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Ordered algebraic structures --- Lie algebras --- Algèbres de Lie --- Infinite dimensional Lie algebras --- Algèbres de Lie
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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
Infinite dimensional Lie algebras. --- Conformal field theory. --- Lie algebras. --- Mathematical physics. --- Moduli spaces. --- Riemann surfaces.
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This book constitutes the proceedings of the 2000 Howard conference on "Infinite Dimensional Lie Groups in Geometry and Representation Theory". It presents some important recent developments in this area. It opens with a topological characterization of regular groups, treats among other topics the integrability problem of various infinite dimensional Lie algebras, presents substantial contributions to important subjects in modern geometry, and concludes with interesting applications to representation theory. The book should be a new source of inspiration for advanced graduate students and esta
Infinite dimensional Lie algebras --- Infinite groups --- Infinite-dimensional manifolds --- Lie groups
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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
Infinite dimensional Lie algebras. --- Conformal field theory. --- Lie algebras. --- Mathematical physics. --- Moduli spaces. --- Riemann surfaces.
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