Описание: This is the English translation of Bourbaki's text Groupes et AlgГЁbres de Lie, Chapters 7 to 9. It completes the previously published translations of Chapters 1 to 3 (3-540-64242-0) and 4 to 6 (3-540-42650-7) by covering the structure and representation theory of semi-simple Lie algebras and compact Lie groups. Chapter 7 deals with Cartan subalgebras of Lie algebras, regular elements and conjugacy theorems. Chapter 8 begins with the structure of split semi-simple Lie algebras and their root systems. It goes on to describe the finite-dimensional modules for such algebras, including the character formula of Hermann Weyl. It concludes with the theory of Chevalley orders. Chapter 9 is devoted to the theory of compact Lie groups, beginning with a discussion of their maximal tori, root systems and Weyl groups. It goes on to describe the representation theory of compact Lie groups, including the application of integration to establish Weyl's formula in this context. The chapter concludes with a discussion of the actions of compact Lie groups on manifolds. The nine chapters together form the most comprehensive text available on the theory of Lie groups and Lie algebras.
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: From the reviews of the French edition: "This is a rich and useful volume. The material it treats has relevance well beyond the theory of Lie groups and algebras, ranging from the geometry of regular polytopes and paving problems to current work on finite simple groups having a (B,N)-pair structure, or "Tits systems". A historical note provides a survey of the contexts in which groups generated by reflections have arisen. A brief introduction includes almost the only other mention of Lie groups and algebras to be found in the volume. Thus the presentation here is really quite independent of Lie theory. The choice of such an approach makes for an elegant, self-contained treatment of some highly interesting mathematics, which can be read with profit and with relative ease by a very wide circle of readers (and with delight by many, if the reviewer is at all representative)."(G.B. Seligman in MathReviews)
Автор: Tauvel Patrice, Yu Rupert W.T. Название: Lie Algebras and Algebraic Groups ISBN: 3540241701 ISBN-13(EAN): 9783540241706 Издательство: Springer Рейтинг: Цена: 13859 р. Наличие на складе: Поставка под заказ.
Описание: The theory of Lie algebras and algebraic groups has been an area of active research for the last 50 years. It intervenes in many different areas of mathematics: for example invariant theory, Poisson geometry, harmonic analysis, mathematical physics. The aim of this book is to assemble in a single volume the algebraic aspects of the theory, so as to present the foundations of the theory in characteristic zero. Detailed proofs are included and some recent results are discussed in the final chapters. All the prerequisites on commutative algebra and algebraic geometry are included.
Описание: With roots in the nineteenth century, Lie theory has since found many and varied applications in mathematics and mathematical physics, to the point where it is now regarded as a classical branch of mathematics in its own right. This graduate text focuses on the study of semisimple Lie algebras, developing the necessary theory along the way. The material covered ranges from basic definitions of Lie groups to the classification of finite-dimensional representations of semisimple Lie algebras. Written in an informal style, this is a contemporary introduction to the subject which emphasizes the main concepts of the proofs and outlines the necessary technical details, allowing the material to be conveyed concisely. Based on a lecture course given by the author at the State University of New York at Stony Brook, the book includes numerous exercises and worked examples and is ideal for graduate courses on Lie groups and Lie algebras.
Описание: This book has grown out of a set of lecture notes I had prepared for a course on Lie groups in 1966. When I lectured again on the subject in 1972, I revised the notes substantially. It is the revised version that is now appearing in book form. The theory of Lie groups plays a fundamental role in many areas of mathematics. There are a number of books on the subject currently available -most notably those of Chevalley, Jacobson, and Bourbaki-which present various aspects of the theory in great depth. However, 1 feei there is a need for a single book in English which develops both the algebraic and analytic aspects of the theory and which goes into the representation theory of semi simple Lie groups and Lie algebras in detail. This book is an attempt to fiii this need. It is my hope that this book will introduce the aspiring graduate student as well as the nonspecialist mathematician to the fundamental themes of the subject. I have made no attempt to discuss infinite-dimensional representations. This is a very active field, and a proper treatment of it would require another volume (if not more) of this size. However, the reader who wants to take up this theory will find that this book prepares him reasonably well for that task."
Автор: Bourbaki Название: Lie Groups and Lie Algebras ISBN: 3540642420 ISBN-13(EAN): 9783540642428 Издательство: Springer Цена: 6351 р. Наличие на складе: Поставка под заказ.
Описание: This is the softcover reprint of the English translation of 1975 (available from Springer since 1989) of the first 3 chapters of Bourbaki's 'Groupes et algebres de
Lie'. The first chapter describes the theory of Lie algebras, their derivations, their representations and their enveloping algebras. In Ch.
2, free Lie algebras are introduced in
order to discuss the exponential, logarithmic and the Hausdorff series. Ch. 3 deals with the theory of Lie groups over R and C and ultrametric fields.
It describes the
connections between their local and global properties, and the properties of their Lie algebras. It is one of the very best references on this subject.
Автор: Bourbaki, Nicolas Название: Lie groups and lie algebras ISBN: 354068851X ISBN-13(EAN): 9783540688518 Издательство: Springer Рейтинг: Цена: 6929 р. Наличие на складе: Поставка под заказ.
Описание: Covers the structure and representation theory of semi-simple Lie algebras and compact Lie groups. This book deals with Cartan subalgebras of Lie algebras, regular elements and conjugacy theorems. It presents the structure of split semi-simple Lie algebras and their root systems.
Автор: Bourbaki, Nicolas Название: Lie groups and lie algebras ISBN: 3540691715 ISBN-13(EAN): 9783540691716 Издательство: Springer Рейтинг: Цена: 6929 р. Наличие на складе: Поставка под заказ.
Описание: Covers topics ranging from the geometry of regular polytopes and paving problems to work on finite simple groups having a (B,N)-pair structure, or `Tits systems`. This book also provides a survey of the contexts in which groups generated by reflections have arisen.
Описание: This book is intended for graduate students in Physics, especially Elementary Particle Physics. It gives an introduction to group theory for physicists with a focus on Lie groups and Lie algebras.
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.
Описание: This research monograph introduces some new aspects to the theory of harmonic functions and related topics. The authors study the analytic algebraic structures of the space of bounded harmonic functions on locally compact groups and its non-commutative analogue, the space of harmonic functionals on Fourier algebras. Both spaces are shown to be the range of a contractive projection on a von Neumann algebra and therefore admit Jordan algebraic structures. This provides a natural setting to apply recent results from non-associative analysis, semigroups and Fourier algebras. Topics discussed include Poisson representations, Poisson spaces, quotients of Fourier algebras and the Murray-von Neumann classification of harmonic functionals.
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