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| Author | : H. Strade |
| Publisher | : CRC Press |
| Total Pages | : 321 |
| Release | : 2020-08-12 |
| Genre | : Mathematics |
| ISBN | : 1000146820 |
Download Modular Lie Algebras and their Representations Book in PDF, ePub and Kindle
This book presents an introduction to the structure and representation theory of modular Lie algebras over fields of positive characteristic. It introduces the beginner to the theory of modular Lie algebras and is meant to be a reference text for researchers.
| Author | : H. Strade |
| Publisher | : CRC Press |
| Total Pages | : 318 |
| Release | : 2020-08-11 |
| Genre | : Mathematics |
| ISBN | : 1000103390 |
Download Modular Lie Algebras and their Representations Book in PDF, ePub and Kindle
This book presents an introduction to the structure and representation theory of modular Lie algebras over fields of positive characteristic. It introduces the beginner to the theory of modular Lie algebras and is meant to be a reference text for researchers.
| Author | : Jean-Philippe Anker |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 341 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 0817681922 |
Download Lie Theory Book in PDF, ePub and Kindle
* First of three independent, self-contained volumes under the general title, "Lie Theory," featuring original results and survey work from renowned mathematicians. * Contains J. C. Jantzen's "Nilpotent Orbits in Representation Theory," and K.-H. Neeb's "Infinite Dimensional Groups and their Representations." * Comprehensive treatments of the relevant geometry of orbits in Lie algebras, or their duals, and the correspondence to representations. * Should benefit graduate students and researchers in mathematics and mathematical physics.
| Author | : Seok-Jin Kang |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 242 |
| Release | : 1996 |
| Genre | : Mathematics |
| ISBN | : 0821805126 |
Download Lie Algebras and Their Representations Book in PDF, ePub and Kindle
Over the past 30 years, exciting developments in diverse areas of the theory of Lie algebras and their representations have been observed. The symposium covered topics such as Lie algebras and combinatorics, crystal bases for quantum groups, quantum groups and solvable lattice models, and modular and infinite-dimensional Lie algebras. In this volume, readers will find several excellent expository articles and research papers containing many significant new results in this area.
| Author | : V.S. Varadarajan |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 444 |
| Release | : 2013-04-17 |
| Genre | : Mathematics |
| ISBN | : 1461211263 |
Download Lie Groups, Lie Algebras, and Their Representations Book in PDF, ePub and Kindle
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.
| Author | : Geoge B. Seligman |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 175 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 3642949851 |
Download Modular Lie Algebras Book in PDF, ePub and Kindle
The study of the structure of Lie algebras over arbitrary fields is now a little more than thirty years old. The first papers, to my know ledge, which undertook this study as an end in itself were those of JACOBSON (" Rational methods in the theory of Lie algebras ") in the Annals, and of LANDHERR ("Uber einfache Liesche Ringe") in the Hamburg Abhandlungen, both in 1935. Over fields of characteristic zero, these thirty years have seen the ideas and results inherited from LIE, KILLING, E. CARTAN and WEYL developed and given new depth, meaning and elegance by many contributors. Much of this work is presented in [47, 64, 128 and 234] of the bibliography. For those who find the rationalization for the study of Lie algebras in their connections with Lie groups, satisfying counterparts to these connections have been found over general non-modular fields, with the substitution of the formal groups of BOCHNER [40] (see also DIEUDONNE [108]), or that of the algebraic linear groups of CHEVALLEY [71], for the usual Lie group. In particular, the relation with algebraic linear groups has stimulated the study of Lie algebras of linear transformations. When one admits to consideration Lie algebras over a base field of positive characteristic (such are the algebras to which the title of this monograph refers), he encounters a new and initially confusing scene.
| Author | : Alexander A. Kirillov |
| Publisher | : Cambridge University Press |
| Total Pages | : 237 |
| Release | : 2008-07-31 |
| Genre | : Mathematics |
| ISBN | : 0521889693 |
Download An Introduction to Lie Groups and Lie Algebras Book in PDF, ePub and Kindle
Contemporary introduction to semisimple Lie algebras; concise and informal, with numerous exercises and examples
| Author | : A. Broer |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 455 |
| Release | : 2013-03-09 |
| Genre | : Mathematics |
| ISBN | : 9401591318 |
Download Representation Theories and Algebraic Geometry Book in PDF, ePub and Kindle
The 12 lectures presented in Representation Theories and Algebraic Geometry focus on the very rich and powerful interplay between algebraic geometry and the representation theories of various modern mathematical structures, such as reductive groups, quantum groups, Hecke algebras, restricted Lie algebras, and their companions. This interplay has been extensively exploited during recent years, resulting in great progress in these representation theories. Conversely, a great stimulus has been given to the development of such geometric theories as D-modules, perverse sheafs and equivariant intersection cohomology. The range of topics covered is wide, from equivariant Chow groups, decomposition classes and Schubert varieties, multiplicity free actions, convolution algebras, standard monomial theory, and canonical bases, to annihilators of quantum Verma modules, modular representation theory of Lie algebras and combinatorics of representation categories of Harish-Chandra modules.
| Author | : E.A. de Kerf |
| Publisher | : Elsevier |
| Total Pages | : 553 |
| Release | : 1997-10-30 |
| Genre | : Science |
| ISBN | : 9780080535463 |
Download Lie Algebras, Part 2 Book in PDF, ePub and Kindle
This is the long awaited follow-up to Lie Algebras, Part I which covered a major part of the theory of Kac-Moody algebras, stressing primarily their mathematical structure. Part II deals mainly with the representations and applications of Lie Algebras and contains many cross references to Part I. The theoretical part largely deals with the representation theory of Lie algebras with a triangular decomposition, of which Kac-Moody algebras and the Virasoro algebra are prime examples. After setting up the general framework of highest weight representations, the book continues to treat topics as the Casimir operator and the Weyl-Kac character formula, which are specific for Kac-Moody algebras. The applications have a wide range. First, the book contains an exposition on the role of finite-dimensional semisimple Lie algebras and their representations in the standard and grand unified models of elementary particle physics. A second application is in the realm of soliton equations and their infinite-dimensional symmetry groups and algebras. The book concludes with a chapter on conformal field theory and the importance of the Virasoro and Kac-Moody algebras therein.
| Author | : K. Erdmann |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 254 |
| Release | : 2006-09-28 |
| Genre | : Mathematics |
| ISBN | : 1846284902 |
Download Introduction to Lie Algebras Book in PDF, ePub and Kindle
Lie groups and Lie algebras have become essential to many parts of mathematics and theoretical physics, with Lie algebras a central object of interest in their own right. This book provides an elementary introduction to Lie algebras based on a lecture course given to fourth-year undergraduates. The only prerequisite is some linear algebra and an appendix summarizes the main facts that are needed. The treatment is kept as simple as possible with no attempt at full generality. Numerous worked examples and exercises are provided to test understanding, along with more demanding problems, several of which have solutions. Introduction to Lie Algebras covers the core material required for almost all other work in Lie theory and provides a self-study guide suitable for undergraduate students in their final year and graduate students and researchers in mathematics and theoretical physics.
