Lie Algebras Part 2
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Lie Algebras Part 2
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Author : E.A. de Kerf
language : en
Publisher: Elsevier
Release Date : 1997-10-30
Lie Algebras Part 2 written by E.A. de Kerf and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-10-30 with Science categories.
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.
Lie Groups Lie Algebras And Representations
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Author : Brian Hall
language : en
Publisher: Springer
Release Date : 2015-05-11
Lie Groups Lie Algebras And Representations written by Brian Hall and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-05-11 with Mathematics categories.
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 Poincaré–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
Lie Groups Lie Algebras
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Author : Melvin Hausner
language : en
Publisher: CRC Press
Release Date : 1968
Lie Groups Lie Algebras written by Melvin Hausner and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1968 with Lie algebras categories.
Polished lecture notes provide a clean and usefully detailed account of the standard elements of the theory of Lie groups and algebras. Following nineteen pages of preparatory material, Part I (seven brief chapters) treats "Lie groups and their Lie algebras"; Part II (seven chapters) treats "complex semi-simple Lie algebras"; Part III (two chapters) treats "real semi-simple Lie algebras". The page design is intimidatingly dense, the exposition very much in the familiar "definition/lemma/proof/theorem/proof/remark" mode, and there are no exercises or bibliography. (NW) Annotation copyrighted by Book News, Inc., Portland, OR
Lie Groups And Lie Algebras I
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Author : V.V. Gorbatsevich
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-12-01
Lie Groups And Lie Algebras I written by V.V. Gorbatsevich and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-12-01 with Mathematics categories.
From the reviews: "..., the book must be of great help for a researcher who already has some idea of Lie theory, wants to employ it in his everyday research and/or teaching, and needs a source for customary reference on the subject. From my viewpoint, the volume is perfectly fit to serve as such a source, ... On the whole, it is quite a pleasure, after making yourself comfortable in that favourite office armchair of yours, just to keep the volume gently in your hands and browse it slowly and thoughtfully; and after all, what more on Earth can one expect of any book?" --The New Zealand Mathematical Society Newsletter
Lie Groups And Lie Algebras
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Author : N. Bourbaki
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-09-30
Lie Groups And Lie Algebras written by N. Bourbaki and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-09-30 with Mathematics categories.
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’". --G.B. Seligman in MathReviews.
Lie Groups And Lie Algebras I
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Author : V.V. Gorbatsevich
language : en
Publisher: Springer Science & Business Media
Release Date : 1996-12-18
Lie Groups And Lie Algebras I written by V.V. Gorbatsevich and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996-12-18 with Mathematics categories.
From the reviews: "..., the book must be of great help for a researcher who already has some idea of Lie theory, wants to employ it in his everyday research and/or teaching, and needs a source for customary reference on the subject. From my viewpoint, the volume is perfectly fit to serve as such a source, ... On the whole, it is quite a pleasure, after making yourself comfortable in that favourite office armchair of yours, just to keep the volume gently in your hands and browse it slowly and thoughtfully; and after all, what more on Earth can one expect of any book?" --The New Zealand Mathematical Society Newsletter
Lie Groups And Lie Algebras I
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Author : V.V. Gorbatsevich
language : en
Publisher: Springer
Release Date : 1993-04-15
Lie Groups And Lie Algebras I written by V.V. Gorbatsevich and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993-04-15 with Mathematics categories.
From the reviews: "..., the book must be of great help for a researcher who already has some idea of Lie theory, wants to employ it in his everyday research and/or teaching, and needs a source for customary reference on the subject. From my viewpoint, the volume is perfectly fit to serve as such a source, ... On the whole, it is quite a pleasure, after making yourself comfortable in that favourite office armchair of yours, just to keep the volume gently in your hands and browse it slowly and thoughtfully; and after all, what more on Earth can one expect of any book?" --The New Zealand Mathematical Society Newsletter
Lie Groups And Lie Algebras
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Author : N. Bourbaki
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-09-30
Lie Groups And Lie Algebras written by N. Bourbaki and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-09-30 with Mathematics categories.
This is the soft cover reprint of the English translation of Bourbaki's text Groupes et Algèbres de Lie, Chapters 7 to 9. It covers the structure and representation theory of semi-simple Lie algebras and compact Lie groups.
Classification And Identification Of Lie Algebras
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Author : Libor Snobl
language : en
Publisher:
Release Date : 2014
Classification And Identification Of Lie Algebras written by Libor Snobl and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014 with Lie algebras categories.
Cover -- Title page -- Contents -- Preface -- Acknowledgments -- Part 1. General theory -- Introduction and motivation -- Basic concepts -- Invariants of the coadjoint representation of a Lie algebra -- Part 2. Recognition of a Lie algebra given by its structure constants -- Identification of Lie algebras through the use of invariants -- Decomposition into a direct sum -- Levi decomposition. Identification of the radical and Levi factor -- The nilradical of a Lie algebra -- Part 3. Nilpotent, solvable and Levi decomposable Lie algebras -- Nilpotent Lie algebras -- Solvable Lie algebras and their nilradicals -- Solvable Lie algebras with abelian nilradicals -- Solvable Lie algebras with Heisenberg nilradical -- Solvable Lie algebras with Borel nilradicals -- Solvable Lie algebras with filiform and quasifiliform nilradicals -- Levi decomposable algebras -- Part 4. Low-dimensional Lie algebras -- Structure of the lists of low-dimensional Lie algebras -- Lie algebras up to dimension 3 -- Four-dimensional Lie algebras -- Five-dimensional Lie algebras -- Six-dimensional Lie algebras -- Bibliography -- Index -- Back Cover
Introduction To Lie Algebras And Representation Theory
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Author : J.E. Humphreys
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Introduction To Lie Algebras And Representation Theory written by J.E. Humphreys and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
This book is designed to introduce the reader to the theory of semisimple Lie algebras over an algebraically closed field of characteristic 0, with emphasis on representations. A good knowledge of linear algebra (including eigenvalues, bilinear forms, euclidean spaces, and tensor products of vector spaces) is presupposed, as well as some acquaintance with the methods of abstract algebra. The first four chapters might well be read by a bright undergraduate; however, the remaining three chapters are admittedly a little more demanding. Besides being useful in many parts of mathematics and physics, the theory of semisimple Lie algebras is inherently attractive, combining as it does a certain amount of depth and a satisfying degree of completeness in its basic results. Since Jacobson's book appeared a decade ago, improvements have been made even in the classical parts of the theory. I have tried to incor porate some of them here and to provide easier access to the subject for non-specialists. For the specialist, the following features should be noted: (I) The Jordan-Chevalley decomposition of linear transformations is emphasized, with "toral" subalgebras replacing the more traditional Cartan subalgebras in the semisimple case. (2) The conjugacy theorem for Cartan subalgebras is proved (following D. J. Winter and G. D. Mostow) by elementary Lie algebra methods, avoiding the use of algebraic geometry.