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.
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.
Описание: This first part of a two-volume set offers a modern account of the representation theory of finite dimensional associative algebras over an algebraically closed field. The authors present this topic from the perspective of linear representations of finite-oriented graphs (quivers) and homological algebra. The self-contained treatment constitutes an elementary, up-to-date introduction to the subject using, on the one hand, quiver-theoretical techniques and, on the other, tilting theory and integral quadratic forms. Key features include many illustrative examples, plus a large number of end-of-chapter exercises. The detailed proofs make this work suitable both for courses and seminars, and for self-study. The volume will be of great interest to graduate students beginning research in the representation theory of algebras and to mathematicians from other fields.
Описание: Being the first monograph devoted to this subject, the book addresses the classification problem for semisimple Hopf algebras, a field that has attracted considerable attention in the last years. The special approach to this problem taken here is via semidirect product decompositions into Yetter-Drinfel'd Hopf algebras and group rings of cyclic groups of prime order. One of the main features of the book is a complete treatment of the structure theory for such Yetter-Drinfel'd Hopf algebras.
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: This book reproduces J-P. Serre's 1964 Harvard lectures. The aim is to introduce the reader to the "Lie dictionary": Lie algebras and Lie groups. Special features of the presentation are its emphasis on formal groups (in the Lie group part) and the use of analytic manifolds on p-adic fields. Some knowledge of algebra and calculus is required of the reader, but the text is easily accessible to graduate students, and to mathematicians at large.
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, 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.
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