Symmetries, Lie Algebras and Representations, Fuchs/Schweigert
Автор: Johnson D.L. Название: Symmetries ISBN: 1852332700 ISBN-13(EAN): 9781852332709 Издательство: Springer Рейтинг: Цена: 3652 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: The main object of study for this book is geometry, with group theory providing an appropriate language in which to express geometrical ideas. Key features include: An overview of the preliminaries from group theory and geometry Coverage of the discrete subgroups of the Euclidean group A clear and complete derivation and classification of the 17 plane crystallographic groups Tessellations of various spaces (they are constructed, described and classified) A brief introduction to hyperbolic geometry. Each chapter contains a number of exercises, most with solutions, and suggestions for background, alternative and further reading. The author's accessible and down-to-earth approach make this an ideal introduction for readers in the second or third year of a mathematics undergraduate course. It is also recommended for mechanical engineers, architects, physicists and crystallographers needing an understanding of 3-dimensional geometry, symmetry and trigonometry.
Автор: Serre Jean-Pierre, Jones G.A. Название: Complex Semisimple Lie Algebras ISBN: 3540678271 ISBN-13(EAN): 9783540678274 Издательство: Springer Рейтинг: Цена: 5224 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: These notes, already well known in their original French edition, give the basic theory of semisimple Lie algebras over the complex numbers including the basic classification theorem. The author begins with a summary of the general properties of nilpotent, solvable, and semisimple Lie algebras. Subsequent chapters introduce Cartan subalgebras, root systems, and representation theory. The theory is illustrated by using the example of sln; in particular, the representation theory of sl2 is completely worked out. The last chapter discusses the connection between Lie algebras and Lie groups, and is intended to guide the reader towards further study.
Описание: Introduces the reader to the theory of semisimple Lie algebras over an algebraically closed field of characteristic 0, with emphasis on representations. Here, a good knowledge of linear algebra is presupposed, as well as some acquaintance with the methods of abstract algebra.
Автор: Erdmann Название: Introduction to Lie Algebras ISBN: 1846280400 ISBN-13(EAN): 9781846280405 Издательство: Springer Рейтинг: Цена: 3652 р. Наличие на складе: Поставка под заказ.
Описание: Lie groups and Lie algebras have become essential to many parts of mathematics and theoretical physics. This book provides an elementary introduction to Lie algebras based on a lecture course given to fourth-year undergraduates. It also acts as a self-study guide for graduate students and researchers in mathematics and theoretical physics.
Описание: Describes an original formalism based on mirror symmetries of Lie groups, Lie algebras and Homogeneous spaces. This book should is useful for researchers in Lie Groups, Lie Algebras, Differential Geometry and their applications, as well as for other postgraduate and advanced graduate students in mathematics.
Описание: This book addresses Lie groups, Lie algebras, and representation theory. In order to keep the prerequisites to a minimum, the author restricts attention to matrix Lie groups and Lie algebras. This approach keeps the discussion concrete, allows the reader to get to the heart of the subject quickly, and covers all of the most interesting examples. The book also introduces the often-intimidating machinery of roots and the Weyl group in a gradual way, using examples and representation theory as motivation. The text is divided into two parts. The first covers Lie groups and Lie algebras and the relationship between them, along with basic representation theory. The second part covers the theory of semisimple Lie groups and Lie algebras, beginning with a detailed analysis of the representations of SU(3). The author illustrates the general theory with numerous images pertaining to Lie algebras of rank two and rank three, including images of root systems, lattices of dominant integral weights, and weight diagrams. This book is sure to become a standard textbook for graduate students in mathematics and physics with little or no prior exposure to Lie theory. Brian Hall is an Associate Professor of Mathematics at the University of Notre Dame.
Автор: Henderson Название: Representations of Lie Algebras ISBN: 1107653614 ISBN-13(EAN): 9781107653610 Издательство: Cambridge Academ Рейтинг: Цена: 4945 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This bold and refreshing approach to Lie algebras assumes only modest prerequisites (linear algebra up to the Jordan canonical form and a basic familiarity with groups and rings), yet it reaches a major result in representation theory: the highest-weight classification of irreducible modules of the general linear Lie algebra. The author's exposition is focused on this goal rather than aiming at the widest generality and emphasis is placed on explicit calculations with bases and matrices. The book begins with a motivating chapter explaining the context and relevance of Lie algebras and their representations and concludes with a guide to further reading. Numerous examples and exercises with full solutions are included. Based on the author's own introductory course on Lie algebras, this book has been thoroughly road-tested by advanced undergraduate and beginning graduate students and it is also suited to individual readers wanting an introduction to this important area of mathematics.
Описание: Surveying the most influential developments in the field, this proceedings reviews the latest research on algebras and their representations, commutative and
non-commutative rings, modules, conformal algebras, and torsion theories. The volume collects stimulating discussions from world-renowned names including Tsit-Yuen Lam, Larry Levy,
Barbara Osofsky, and Patrick Smith.
Описание: Attempts to take us up to the point where we can find our way in the original literature. This book presents some basic material and some insights of the theory. It includes proofs for statements which in the authors` opinions are elementary, those which help further understanding.
Описание: The modular representation theory of Iwahori-Hecke algebras and this theory's connection to groups of Lie type is an area of rapidly expanding interest; it is one that has also seen a number of breakthroughs in recent years. In classifying the irreducible representations of Iwahori-Hecke algebras at roots of unity, this book is a particularly valuable addition to current research in this field. Using the framework provided by the Kazhdan-Lusztig theory of cells, the authors develop an analogue of James' (1970) characteristic-free'' approach to the representation theory of Iwahori-Hecke algebras in general. Presenting a systematic and unified treatment of representations of Hecke algebras at roots of unity, this book is unique in its approach and includes new results that have not yet been published in book form. It also serves as background reading to further active areas of current research such as the theory of affine Hecke algebras and Cherednik algebras. The main results of this book are obtained by an interaction of several branches of mathematics, namely the theory of Fock spaces for quantum affine Lie algebras and Ariki's theorem, the combinatorics of crystal bases, the theory of Kazhdan-Lusztig bases and cells, and computational methods. This book will be of use to researchers and graduate students in representation theory as well as any researchers outside of the field with an interest in Hecke algebras.
Описание: This is an all-encompassing and exhaustive exposition of the theory of infinite-dimensional Unitary Representations of Locally Compact Groups and its generalization to representations of Banach algebras. The presentation is detailed, accessible, and self-contained (except for some elementary knowle
Описание: Modern notions and important tools of classical mechanics are used in the study of concrete examples that model physically significant molecular and atomic systems. The parametric nature of these examples leads naturally to the study of the major qualitative changes of such systems (metamorphoses) as the parameters are varied. The symmetries of these systems, discrete or continuous, exact or approximate, are used to simplify the problem through a number of mathematical tools and techniques like normalization and reduction. The book moves gradually from finding relative equilibria using symmetry, to the Hamiltonian Hopf bifurcation and its relation to monodromy and, finally, to generalizations of monodromy.
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