Nilpotent Lie Groups

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Quantization on Nilpotent Lie Groups

Author : Veronique Fischer
Publisher : Birkhäuser
ISBN 13 : 3319295586
Total Pages : 568 pages
Book Rating : 4.3/5 (192 download)

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Book Synopsis Quantization on Nilpotent Lie Groups by : Veronique Fischer

Download or read book Quantization on Nilpotent Lie Groups written by Veronique Fischer and published by Birkhäuser. This book was released on 2016-03-08 with total page 568 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a consistent development of the Kohn-Nirenberg type global quantization theory in the setting of graded nilpotent Lie groups in terms of their representations. It contains a detailed exposition of related background topics on homogeneous Lie groups, nilpotent Lie groups, and the analysis of Rockland operators on graded Lie groups together with their associated Sobolev spaces. For the specific example of the Heisenberg group the theory is illustrated in detail. In addition, the book features a brief account of the corresponding quantization theory in the setting of compact Lie groups. The monograph is the winner of the 2014 Ferran Sunyer i Balaguer Prize.

Unipotent and Nilpotent Classes in Simple Algebraic Groups and Lie Algebras

Author : Martin W. Liebeck
Publisher : American Mathematical Soc.
ISBN 13 : 0821869205
Total Pages : 394 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Unipotent and Nilpotent Classes in Simple Algebraic Groups and Lie Algebras by : Martin W. Liebeck

Download or read book Unipotent and Nilpotent Classes in Simple Algebraic Groups and Lie Algebras written by Martin W. Liebeck and published by American Mathematical Soc.. This book was released on 2012-01-25 with total page 394 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book concerns the theory of unipotent elements in simple algebraic groups over algebraically closed or finite fields, and nilpotent elements in the corresponding simple Lie algebras. These topics have been an important area of study for decades, with applications to representation theory, character theory, the subgroup structure of algebraic groups and finite groups, and the classification of the finite simple groups. The main focus is on obtaining full information on class representatives and centralizers of unipotent and nilpotent elements. Although there is a substantial literature on this topic, this book is the first single source where such information is presented completely in all characteristics. In addition, many of the results are new--for example, those concerning centralizers of nilpotent elements in small characteristics. Indeed, the whole approach, while using some ideas from the literature, is novel, and yields many new general and specific facts concerning the structure and embeddings of centralizers.

Nilpotent Lie Algebras

Author : M. Goze
Publisher : Springer Science & Business Media
ISBN 13 : 9401724326
Total Pages : 350 pages
Book Rating : 4.4/5 (17 download)

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Book Synopsis Nilpotent Lie Algebras by : M. Goze

Download or read book Nilpotent Lie Algebras written by M. Goze and published by Springer Science & Business Media. This book was released on 2013-11-27 with total page 350 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is devoted to the theory of nilpotent Lie algebras and their applications. Nilpotent Lie algebras have played an important role over the last years both in the domain of algebra, considering its role in the classification problems of Lie algebras, and in the domain of differential geometry. Among the topics discussed here are the following: cohomology theory of Lie algebras, deformations and contractions, the algebraic variety of the laws of Lie algebras, the variety of nilpotent laws, and characteristically nilpotent Lie algebras in nilmanifolds. Audience: This book is intended for graduate students specialising in algebra, differential geometry and in theoretical physics and for researchers in mathematics and in theoretical physics.

Structure and Geometry of Lie Groups

Author : Joachim Hilgert
Publisher : Springer Science & Business Media
ISBN 13 : 0387847944
Total Pages : 742 pages
Book Rating : 4.3/5 (878 download)

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Book Synopsis Structure and Geometry of Lie Groups by : Joachim Hilgert

Download or read book Structure and Geometry of Lie Groups written by Joachim Hilgert and published by Springer Science & Business Media. This book was released on 2011-11-06 with total page 742 pages. Available in PDF, EPUB and Kindle. Book excerpt: This self-contained text is an excellent introduction to Lie groups and their actions on manifolds. The authors start with an elementary discussion of matrix groups, followed by chapters devoted to the basic structure and representation theory of finite dimensinal Lie algebras. They then turn to global issues, demonstrating the key issue of the interplay between differential geometry and Lie theory. Special emphasis is placed on homogeneous spaces and invariant geometric structures. The last section of the book is dedicated to the structure theory of Lie groups. Particularly, they focus on maximal compact subgroups, dense subgroups, complex structures, and linearity. This text is accessible to a broad range of mathematicians and graduate students; it will be useful both as a graduate textbook and as a research reference.

A Course in Group Theory

Author : J. F. Humphreys
Publisher : Oxford University Press, USA
ISBN 13 : 9780198534594
Total Pages : 296 pages
Book Rating : 4.5/5 (345 download)

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Book Synopsis A Course in Group Theory by : J. F. Humphreys

Download or read book A Course in Group Theory written by J. F. Humphreys and published by Oxford University Press, USA. This book was released on 1996 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt: Each chapter ends with a summary of the material covered and notes on the history and development of group theory.

Representations of Nilpotent Lie Groups and their Applications: Volume 1, Part 1, Basic Theory and Examples

Author : Laurence Corwin
Publisher : Cambridge University Press
ISBN 13 : 9780521604956
Total Pages : 280 pages
Book Rating : 4.6/5 (49 download)

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Book Synopsis Representations of Nilpotent Lie Groups and their Applications: Volume 1, Part 1, Basic Theory and Examples by : Laurence Corwin

Download or read book Representations of Nilpotent Lie Groups and their Applications: Volume 1, Part 1, Basic Theory and Examples written by Laurence Corwin and published by Cambridge University Press. This book was released on 2004-06-03 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt: There has been no exposition of group representations and harmonic analysis suitable for graduate students for over twenty years. In this, the first of two projected volumes, the authors remedy the situation by surveying all the basic theory developed since the pioneering work of Kirillov in 1958, and consolidating more recent results. Topics covered include basic Kirillov theory, algorithms for parametrizing all coadjoint orbits. The authors have not only given here a modern account of all topics necessary for current research, but have also included many computed examples. This volume can serve then either as a handbook for specialists, with a complete, self-contained exposition of major results, or as a textbook suitable for graduate courses in harmonic analysis.

The Theory of Nilpotent Groups

Author : Anthony E. Clement
Publisher : Birkhäuser
ISBN 13 : 3319662139
Total Pages : 318 pages
Book Rating : 4.3/5 (196 download)

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Book Synopsis The Theory of Nilpotent Groups by : Anthony E. Clement

Download or read book The Theory of Nilpotent Groups written by Anthony E. Clement and published by Birkhäuser. This book was released on 2017-11-18 with total page 318 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph presents both classical and recent results in the theory of nilpotent groups and provides a self-contained, comprehensive reference on the topic. While the theorems and proofs included can be found throughout the existing literature, this is the first book to collect them in a single volume. Details omitted from the original sources, along with additional computations and explanations, have been added to foster a stronger understanding of the theory of nilpotent groups and the techniques commonly used to study them. Topics discussed include collection processes, normal forms and embeddings, isolators, extraction of roots, P-localization, dimension subgroups and Lie algebras, decision problems, and nilpotent groups of automorphisms. Requiring only a strong undergraduate or beginning graduate background in algebra, graduate students and researchers in mathematics will find The Theory of Nilpotent Groups to be a valuable resource.

An Introduction to Lie Groups and Lie Algebras

Author : Alexander A. Kirillov
Publisher : Cambridge University Press
ISBN 13 : 0521889693
Total Pages : 237 pages
Book Rating : 4.5/5 (218 download)

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Book Synopsis An Introduction to Lie Groups and Lie Algebras by : Alexander A. Kirillov

Download or read book An Introduction to Lie Groups and Lie Algebras written by Alexander A. Kirillov and published by Cambridge University Press. This book was released on 2008-07-31 with total page 237 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an introduction to semisimple Lie algebras. It is concise and informal, with numerous exercises and examples.

Representations and Nilpotent Orbits of Lie Algebraic Systems

Author : Maria Gorelik
Publisher : Springer Nature
ISBN 13 : 3030235319
Total Pages : 553 pages
Book Rating : 4.0/5 (32 download)

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Book Synopsis Representations and Nilpotent Orbits of Lie Algebraic Systems by : Maria Gorelik

Download or read book Representations and Nilpotent Orbits of Lie Algebraic Systems written by Maria Gorelik and published by Springer Nature. This book was released on 2019-10-18 with total page 553 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume, a celebration of Anthony Joseph’s fundamental influence on classical and quantized representation theory, explores a wide array of current topics in Lie theory by experts in the area. The chapters are based on the 2017 sister conferences titled “Algebraic Modes of Representations,” the first of which was held from July 16-18 at the Weizmann Institute of Science and the second from July 19-23 at the University of Haifa. The chapters in this volume cover a range of topics, including: Primitive ideals Invariant theory Geometry of Lie group actions Quantum affine algebras Yangians Categorification Vertex algebras This volume is addressed to mathematicians who specialize in representation theory and Lie theory, and who wish to learn more about this fascinating subject.

Lie Algebras and Lie Groups

Author : Jean-Pierre Serre
Publisher : Springer
ISBN 13 : 3540706348
Total Pages : 180 pages
Book Rating : 4.5/5 (47 download)

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Book Synopsis Lie Algebras and Lie Groups by : Jean-Pierre Serre

Download or read book Lie Algebras and Lie Groups written by Jean-Pierre Serre and published by Springer. This book was released on 2009-02-07 with total page 180 pages. Available in PDF, EPUB and Kindle. Book excerpt: The main general theorems on Lie Algebras are covered, roughly the content of Bourbaki's Chapter I.I have added some results on free Lie algebras, which are useful, both for Lie's theory itself (Campbell-Hausdorff formula) and for applications to pro-Jrgroups. of time prevented me from including the more precise theory of Lack semisimple Lie algebras (roots, weights, etc.); but, at least, I have given, as a last Chapter, the typical case ofal, . This part has been written with the help of F. Raggi and J. Tate. I want to thank them, and also Sue Golan, who did the typing for both parts. Jean-Pierre Serre Harvard, Fall 1964 Chapter I. Lie Algebras: Definition and Examples Let Ie be a commutativering with unit element, and let A be a k-module, then A is said to be a Ie-algebra if there is given a k-bilinear map A x A~ A (i.e., a k-homomorphism A0" A -+ A). As usual we may define left, right and two-sided ideals and therefore quo tients. Definition 1. A Lie algebra over Ie isan algebrawith the following properties: 1). The map A0i A -+ A admits a factorization A ®i A -+ A2A -+ A i.e., ifwe denote the imageof(x, y) under this map by [x, y) then the condition becomes for all x e k. [x, x)=0 2). (lx, II], z]+ny, z), x) + ([z, xl, til = 0 (Jacobi's identity) The condition 1) implies [x,1/]=-[1/, x).

Nilpotent Lie Groups

Author : Roe W. Goodman
Publisher : Springer
ISBN 13 : 3540375295
Total Pages : 220 pages
Book Rating : 4.5/5 (43 download)

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Book Synopsis Nilpotent Lie Groups by : Roe W. Goodman

Download or read book Nilpotent Lie Groups written by Roe W. Goodman and published by Springer. This book was released on 2006-11-15 with total page 220 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Representations of Nilpotent Lie Groups and Their Applications: Volume 1, Part 1, Basic Theory and Examples

Author : Laurence Corwin
Publisher : Cambridge University Press
ISBN 13 : 9780521604956
Total Pages : 286 pages
Book Rating : 4.6/5 (49 download)

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Book Synopsis Representations of Nilpotent Lie Groups and Their Applications: Volume 1, Part 1, Basic Theory and Examples by : Laurence Corwin

Download or read book Representations of Nilpotent Lie Groups and Their Applications: Volume 1, Part 1, Basic Theory and Examples written by Laurence Corwin and published by Cambridge University Press. This book was released on 1990-08-30 with total page 286 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first exposition of group representations and harmonic analysis for graduates for over twenty years.

Nilpotent Orbits In Semisimple Lie Algebra

Author : William.M. McGovern
Publisher : Routledge
ISBN 13 : 1351428691
Total Pages : 201 pages
Book Rating : 4.3/5 (514 download)

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Book Synopsis Nilpotent Orbits In Semisimple Lie Algebra by : William.M. McGovern

Download or read book Nilpotent Orbits In Semisimple Lie Algebra written by William.M. McGovern and published by Routledge. This book was released on 2017-10-19 with total page 201 pages. Available in PDF, EPUB and Kindle. Book excerpt: Through the 1990s, a circle of ideas emerged relating three very different kinds of objects associated to a complex semisimple Lie algebra: nilpotent orbits, representations of a Weyl group, and primitive ideals in an enveloping algebra. The principal aim of this book is to collect together the important results concerning the classification and properties of nilpotent orbits, beginning from the common ground of basic structure theory. The techniques used are elementary and in the toolkit of any graduate student interested in the harmonic analysis of representation theory of Lie groups. The book develops the Dynkin-Konstant and Bala-Carter classifications of complex nilpotent orbits, derives the Lusztig-Spaltenstein theory of induction of nilpotent orbits, discusses basic topological questions, and classifies real nilpotent orbits. The classical algebras are emphasized throughout; here the theory can be simplified by using the combinatorics of partitions and tableaux. The authors conclude with a survey of advanced topics related to the above circle of ideas. This book is the product of a two-quarter course taught at the University of Washington.

Abstract Lie Algebras

Author : David J. Winter
Publisher : Courier Corporation
ISBN 13 : 048646282X
Total Pages : 162 pages
Book Rating : 4.4/5 (864 download)

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Book Synopsis Abstract Lie Algebras by : David J. Winter

Download or read book Abstract Lie Algebras written by David J. Winter and published by Courier Corporation. This book was released on 2008-01-01 with total page 162 pages. Available in PDF, EPUB and Kindle. Book excerpt: Solid but concise, this account emphasizes Lie algebra's simplicity of theory, offering new approaches to major theorems and extensive treatment of Cartan and related Lie subalgebras over arbitrary fields. 1972 edition.

Introduction to Lie Algebras and Representation Theory

Author : J.E. Humphreys
Publisher : Springer Science & Business Media
ISBN 13 : 1461263980
Total Pages : 189 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Introduction to Lie Algebras and Representation Theory by : J.E. Humphreys

Download or read book Introduction to Lie Algebras and Representation Theory written by J.E. Humphreys and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 189 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Lie Algebras of Finite and Affine Type

Author : Roger William Carter
Publisher : Cambridge University Press
ISBN 13 : 9780521851381
Total Pages : 662 pages
Book Rating : 4.8/5 (513 download)

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Book Synopsis Lie Algebras of Finite and Affine Type by : Roger William Carter

Download or read book Lie Algebras of Finite and Affine Type written by Roger William Carter and published by Cambridge University Press. This book was released on 2005-10-27 with total page 662 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a thorough but relaxed mathematical treatment of Lie algebras.

Lie Algebras

Author : Nathan Jacobson
Publisher : Courier Corporation
ISBN 13 : 0486136795
Total Pages : 348 pages
Book Rating : 4.4/5 (861 download)

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Book Synopsis Lie Algebras by : Nathan Jacobson

Download or read book Lie Algebras written by Nathan Jacobson and published by Courier Corporation. This book was released on 2013-09-16 with total page 348 pages. Available in PDF, EPUB and Kindle. Book excerpt: DIVDefinitive treatment of important subject in modern mathematics. Covers split semi-simple Lie algebras, universal enveloping algebras, classification of irreducible modules, automorphisms, simple Lie algebras over an arbitrary field, etc. Index. /div