Описание: The first edition of this book is a collection of a series of lectures given by Professor Victor Kac at the TIFR, Mumbai, India in December 1985 and January 1986. These lectures focus on the idea of a highest weight representation, which goes through four different incarnations.The first is the canonical commutation relations of the infinite dimensional Heisenberg Algebra (= oscillator algebra). The second is the highest weight representations of the Lie algebra gℓ∞ of infinite matrices, along with their applications to the theory of soliton equations, discovered by Sato and Date, Jimbo, Kashiwara and Miwa. The third is the unitary highest weight representations of the current (= affine Kac-Moody) algebras. These Lie algebras appear in the lectures in connection to the Sugawara construction, which is the main tool in the study of the fourth incarnation of the main idea, the theory of the highest weight representations of the Virasoro algebra. In particular, the book provides a complete proof of the Kac determinant formula, the key result in representation theory of the Virasoro algebra.The second edition of this book incorporates, as its first part, the largely unchanged text of the first edition, while its second part is the collection of lectures on vertex algebras, delivered by Professor Kac at the TIFR in January 2003. The basic idea of these lectures was to demonstrate how the key notions of the theory of vertex algebras -- such as quantum fields, their normal ordered product and lambda-bracket, energy-momentum field and conformal weight, untwisted and twisted representations -- simplify and clarify the constructions of the first edition of the book.This book should be very useful for both mathematicians and physicists. To mathematicians, it illustrates the interaction of the key ideas of the representation theory of infinite dimensional Lie algebras and of the theory of vertex algebras; and to physicists, these theories are turning into an important component of such domains of theoretical physics as soliton theory, conformal field theory, the theory of two-dimensional statistical models, and string theory.
Описание: The first edition of this book is a collection of a series of lectures given by Professor Victor Kac at the TIFR, Mumbai, India in December 1985 and January 1986. These lectures focus on the idea of a highest weight representation, which goes through four different incarnations.The first is the canonical commutation relations of the infinite dimensional Heisenberg Algebra (= oscillator algebra). The second is the highest weight representations of the Lie algebra gℓ∞ of infinite matrices, along with their applications to the theory of soliton equations, discovered by Sato and Date, Jimbo, Kashiwara and Miwa. The third is the unitary highest weight representations of the current (= affine Kac-Moody) algebras. These Lie algebras appear in the lectures in connection to the Sugawara construction, which is the main tool in the study of the fourth incarnation of the main idea, the theory of the highest weight representations of the Virasoro algebra. In particular, the book provides a complete proof of the Kac determinant formula, the key result in representation theory of the Virasoro algebra.The second edition of this book incorporates, as its first part, the largely unchanged text of the first edition, while its second part is the collection of lectures on vertex algebras, delivered by Professor Kac at the TIFR in January 2003. The basic idea of these lectures was to demonstrate how the key notions of the theory of vertex algebras -- such as quantum fields, their normal ordered product and lambda-bracket, energy-momentum field and conformal weight, untwisted and twisted representations -- simplify and clarify the constructions of the first edition of the book.This book should be very useful for both mathematicians and physicists. To mathematicians, it illustrates the interaction of the key ideas of the representation theory of infinite dimensional Lie algebras and of the theory of vertex algebras; and to physicists, these theories are turning into an important component of such domains of theoretical physics as soliton theory, conformal field theory, the theory of two-dimensional statistical models, and string theory.
Автор: V. Dlab; P. Gabriel Название: Representations of Algebras ISBN: 3540074066 ISBN-13(EAN): 9783540074069 Издательство: Springer Рейтинг: Цена: 4884.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Автор: M. Auslander; E. Lluis Название: Representations of Algebras ISBN: 3540111794 ISBN-13(EAN): 9783540111795 Издательство: Springer Рейтинг: Цена: 4884.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: The conference was attended by over one hundred people and the participants included five mathematical generations Professor Mackey`s mathematical father, Marshall Stone, many mathematical children, grandchildren, and at least one mathematical great-grandchild.
The field of vertex operator algebras is an active area of research and plays an integral role in infinite-dimensional Lie theory, string theory, and conformal field theory, and other subdisciplines of mathematics and physics. This book begins with a careful presentation of the theoretical foundations of vertex operator algebras and their modules, and then proceeds to a range of applications. The text features new, original results and a fresh perspective on the important works of many researchers; in particular, it provides a detailed treatment of the concept of a representation'' of a vertex (operator) algebra. Requiring only a familiarity with basic algebra, this broad, self-contained treatment of the core topics in vertex algebras will appeal to graduate students and researchers in both mathematics and physics.
Описание: This text contains an introduction to the recently developed spectral theory of associative rings and Abelian categories. Its applications to the study of irreducible representations of classes of algebras which play an important part in modern mathematical physics are also included.
Автор: Peter Gabriel; B. Keller; A.I. Kostrikin; Andrei V Название: Representations of Finite-Dimensional Algebras ISBN: 3540537325 ISBN-13(EAN): 9783540537328 Издательство: Springer Рейтинг: Цена: 18860.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Aims to offer an outline of the results on representations of finite-dimensional algebras. This monograph provides examples and the background on decomposition theorems, quivers, almost split sequences and derived categories. It includes a survey on representations of tame and wild quivers, lists of critical algebras, and more.
Автор: V.S. Varadarajan Название: Lie Groups, Lie Algebras, and Their Representations ISBN: 1461270162 ISBN-13(EAN): 9781461270164 Издательство: Springer Рейтинг: Цена: 9357.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Автор: Janos Galambos Название: Representations of Real Numbers by Infinite Series ISBN: 354007547X ISBN-13(EAN): 9783540075479 Издательство: Springer Рейтинг: Цена: 3487.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
