Representations of Finite Groups of Lie Type, Francois Digne, Jean Michel

Автор: Francois Digne, Jean Michel
Название: Representations of Finite Groups of Lie Type
ISBN: 1108481485 ISBN-13(EAN): 9781108481489
Издательство: Cambridge Academ
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Цена: 116160.00 T
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Описание: The original edition of this book, written for beginning graduate students, was the first elementary treatment of representation theory of finite groups of Lie type in book form. This second edition features new material to reflect the continuous evolution of the subject, including chapters on Hecke algebras and Green functions.

Автор: Leonhard L. Scott; Jean-Pierre Serre
Название: Linear Representations of Finite Groups
ISBN: 1468494600 ISBN-13(EAN): 9781468494600
Издательство: Springer
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Цена: 52130.00 T
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Описание: This book consists of three parts, rather different in level and purpose. The first part was originally written for quantum chemists. The second part is a course given in 1966 to second-year students of l`Ecole Normale. It completes in a certain sense the first part. The third part is an introduction to Brauer Theory.

Автор: Peter Woit
Название: Quantum Theory, Groups and Representations
ISBN: 3319646109 ISBN-13(EAN): 9783319646107
Издательство: Springer
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Цена: 74530.00 T
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Описание: The level of presentation is attractive to mathematics students looking to learn about both quantum mechanics and representation theory, while also appealing to physics students who would like to know more about the mathematics underlying the subject.

Автор: Hall Brian
Название: Lie Groups, Lie Algebras, and Representations
ISBN: 3319134663 ISBN-13(EAN): 9783319134666
Издательство: Springer
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Цена: 50810.00 T
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Описание:

This textbook treats Lie groups, Lie algebras and their representations in an elementary but fully rigorous fashion requiring minimal prerequisites. In particular, the theory of matrix Lie groups and their Lie algebras is developed using only linear algebra, and more motivation and intuition for proofs is provided than in most classic texts on the subject.

In addition to its accessible treatment of the basic theory of Lie groups and Lie algebras, the book is also noteworthy for including:

• a treatment of the Baker-Campbell-Hausdorff formula and its use in place of the Frobenius theorem to establish deeper results about the relationship between Lie groups and Lie algebras
• motivation for the machinery of roots, weights and the Weyl group via a concrete and detailed exposition of the representation theory of sl(3;C)
• an unconventional definition of semisimplicity that allows for a rapid development of the structure theory of semisimple Lie algebras
• a self-contained construction of the representations of compact groups, independent of Lie-algebraic arguments

The second edition of Lie Groups, Lie Algebras, and Representations contains many substantial improvements and additions, among them: an entirely new part devoted to the structure and representation theory of compact Lie groups; a complete derivation of the main properties of root systems; the construction of finite-dimensional representations of semisimple Lie algebras has been elaborated; a treatment of universal enveloping algebras, including a proof of the Poincar -Birkhoff-Witt theorem and the existence of Verma modules; complete proofs of the Weyl character formula, the Weyl dimension formula and the Kostant multiplicity formula.

Review of the first edition

This is an excellent book. It deserves to, and undoubtedly will, become the standard text for early graduate courses in Lie group theory ... an important addition to the textbook literature ... it is highly recommended.

-- The Mathematical Gazette

Автор: Naihuan Jing, Kailash C. Misra
Название: Representations of Lie Algebras, Quantum Groups and Related Topics
ISBN: 1470436965 ISBN-13(EAN): 9781470436964
Издательство: Mare Nostrum (Eurospan)
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Цена: 116430.00 T
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Описание: Contains the proceedings of the AMS Special Session on Representations of Lie Algebras, Quantum Groups and Related Topics, held in November 2016. The articles cover various aspects of representations of Kac-Moody Lie algebras and their applications, structure of Leibniz algebras and Krichever-Novikov algebras, and related topics.

Автор: Didier Arnal, Bradley Currey
Название: Representations of Solvable Lie Groups: Basic Theory and Examples
ISBN: 1108428096 ISBN-13(EAN): 9781108428095
Издательство: Cambridge Academ
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Цена: 155230.00 T
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Описание: This monograph answers the need for a unified account of the basic theory of unitary group representations, combined with new results, in a style that is broadly accessible for both graduate students and researchers.

Автор: Benson
Название: Representations of Elementary Abelian p -Groups and Vector Bundles
ISBN: 1107174171 ISBN-13(EAN): 9781107174177
Издательство: Cambridge Academ
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Цена: 121440.00 T
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Описание: This is the first book to study representations of elementary abelian groups using vector bundles on projective space. The treatment includes substantial background material from representation theory and algebraic geometry, including an algebraic treatment of the theory of Chern classes.

Автор: Kac Victor G Et Al
Название: Bombay Lectures On Highest Weight Representations Of Infinite Dimensional Lie Algebras (2Nd Edition)
ISBN: 9814522198 ISBN-13(EAN): 9789814522199
Издательство: World Scientific Publishing
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Цена: 33790.00 T
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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.