Theory Of Groups And Symmetries Finite Groups Lie Groups And Lie Algebras

Theory Of Groups And Symmetries Finite Groups Lie Groups And Lie Algebras Book in PDF, ePub and Kindle version is available to download in english. Read online anytime anywhere directly from your device. Click on the download button below to get a free pdf file of Theory Of Groups And Symmetries Finite Groups Lie Groups And Lie Algebras book. This book definitely worth reading, it is an incredibly well-written.

Theory Of Groups And Symmetries: Finite Groups, Lie Groups, And Lie Algebras

Rubakov Valery A,Isaev Alexey P
Theory Of Groups And Symmetries Finite Groups Lie Groups And Lie Algebras Book PDF

Author : Rubakov Valery A,Isaev Alexey P
Publisher : World Scientific
Page : 476 pages
File Size : 54,8 Mb
Release : 2018-03-21
Category : Science
ISBN : 9789813236875

Get Book

Theory Of Groups And Symmetries: Finite Groups, Lie Groups, And Lie Algebras by Rubakov Valery A,Isaev Alexey P Pdf

The book presents the main approaches in study of algebraic structures of symmetries in models of theoretical and mathematical physics, namely groups and Lie algebras and their deformations. It covers the commonly encountered quantum groups (including Yangians). The second main goal of the book is to present a differential geometry of coset spaces that is actively used in investigations of models of quantum field theory, gravity and statistical physics. The third goal is to explain the main ideas about the theory of conformal symmetries, which is the basis of the AdS/CFT correspondence. The theory of groups and symmetries is an important part of theoretical physics. In elementary particle physics, cosmology and related fields, the key role is played by Lie groups and algebras corresponding to continuous symmetries. For example, relativistic physics is based on the Lorentz and Poincare groups, and the modern theory of elementary particles — the Standard Model — is based on gauge (local) symmetry with the gauge group SU(3) x SU(2) x U(1). This book presents constructions and results of a general nature, along with numerous concrete examples that have direct applications in modern theoretical and mathematical physics. Contents: Preface Groups and Transformations Lie Groups Lie Algebras Representations of Groups and Lie Algebras Compact Lie Algebras Root Systems and Classification of Simple Lie Algebras Homogeneous Spaces and their Geometry Solutions to Selected Problems Selected Bibliography References Index Readership: Graduate students and researchers in theoretical physics and mathematical physics. Keywords: Lie Groups;Lie Algebras;Representation Theory;Conformal Symmetries;Yangians;Coset Spaces;Differential Geometry;Casimir Operators;Root Systems;AdS Spaces;Lobachevskian GeometryReview:0

Theory Of Groups And Symmetries: Representations Of Groups And Lie Algebras, Applications

Alexey P Isaev,Valery A Rubakov
Theory Of Groups And Symmetries Representations Of Groups And Lie Algebras Applications Book PDF

Author : Alexey P Isaev,Valery A Rubakov
Publisher : World Scientific
Page : 615 pages
File Size : 45,7 Mb
Release : 2020-07-16
Category : Science
ISBN : 9789811217425

Get Book

Theory Of Groups And Symmetries: Representations Of Groups And Lie Algebras, Applications by Alexey P Isaev,Valery A Rubakov Pdf

This book is a sequel to the book by the same authors entitled Theory of Groups and Symmetries: Finite Groups, Lie Groups, and Lie Algebras.The presentation begins with the Dirac notation, which is illustrated by boson and fermion oscillator algebras and also Grassmann algebra. Then detailed account of finite-dimensional representations of groups SL(2, C) and SU(2) and their Lie algebras is presented. The general theory of finite-dimensional irreducible representations of simple Lie algebras based on the construction of highest weight representations is given. The classification of all finite-dimensional irreducible representations of the Lie algebras of the classical series sℓ(n, C), so(n, C) and sp(2r, C) is exposed.Finite-dimensional irreducible representations of linear groups SL(N, C) and their compact forms SU(N) are constructed on the basis of the Schur-Weyl duality. A special role here is played by the theory of representations of the symmetric group algebra C[Sr] (Schur-Frobenius theory, Okounkov-Vershik approach), based on combinatorics of Young diagrams and Young tableaux. Similar construction is given for pseudo-orthogonal groups O(p, q) and SO(p, q), including Lorentz groups O(1, N-1) and SO(1, N-1), and their Lie algebras, as well as symplectic groups Sp(p, q). The representation theory of Brauer algebra (centralizer algebra of SO(p, q) and Sp(p, q) groups in tensor representations) is discussed.Finally, the covering groups Spin(p, q) for pseudo-orthogonal groups SO↑(p, q) are studied. For this purpose, Clifford algebras in spaces Rp, q are introduced and representations of these algebras are discussed.

Groups and Symmetries

Yvette Kosmann-Schwarzbach
Groups and Symmetries Book PDF

Author : Yvette Kosmann-Schwarzbach
Publisher : Unknown
Page : 0 pages
File Size : 52,7 Mb
Release : 2022
Category : Electronic
ISBN : 3030943615

Get Book

Groups and Symmetries by Yvette Kosmann-Schwarzbach Pdf

Groups and Symmetries: From Finite Groups to Lie Groups presents an introduction to the theory of group representations and its applications in quantum mechanics. Accessible to advanced undergraduates in mathematics and physics as well as beginning graduate students, the text deals with the theory of representations of finite groups, compact groups, linear Lie groups and their Lie algebras, concisely and in one volume. Prerequisites include calculus and linear algebra. This new edition contains an additional chapter that deals with Clifford algebras, spin groups, and the theory of spinors, as well as new sections entitled "Topics in history" comprising notes on the history of the material treated within each chapter. (Taken together, they constitute an account of the development of the theory of groups from its inception in the 18th century to the mid-20th.) References for additional resources and further study are provided in each chapter. All chapters end with exercises of varying degree of difficulty, some of which introduce new definitions and results. The text concludes with a collection of problems with complete solutions making it ideal for both course work and independent study. Key Topics include: Brisk review of the basic definitions of group theory, with examples Representation theory of finite groups: character theory Representations of compact groups using the Haar measure Lie algebras and linear Lie groups Detailed study of SO(3) and SU(2), and their representations Spherical harmonics Representations of SU(3), roots and weights, with quark theory as a consequence of the mathematical properties of this symmetry group Spin groups and spinors.

Groups and Symmetries

Yvette Kosmann-Schwarzbach
Groups and Symmetries Book PDF

Author : Yvette Kosmann-Schwarzbach
Publisher : Springer Science & Business Media
Page : 207 pages
File Size : 54,8 Mb
Release : 2009-10-16
Category : Mathematics
ISBN : 9780387788661

Get Book

Groups and Symmetries by Yvette Kosmann-Schwarzbach Pdf

- Combines material from many areas of mathematics, including algebra, geometry, and analysis, so students see connections between these areas - Applies material to physics so students appreciate the applications of abstract mathematics - Assumes only linear algebra and calculus, making an advanced subject accessible to undergraduates - Includes 142 exercises, many with hints or complete solutions, so text may be used in the classroom or for self study

An Introduction to Lie Groups and Lie Algebras

Alexander A. Kirillov
An Introduction to Lie Groups and Lie Algebras Book PDF

Author : Alexander A. Kirillov
Publisher : Cambridge University Press
Page : 237 pages
File Size : 45,6 Mb
Release : 2008-07-31
Category : Mathematics
ISBN : 9780521889698

Get Book

An Introduction to Lie Groups and Lie Algebras by Alexander A. Kirillov Pdf

Contemporary introduction to semisimple Lie algebras; concise and informal, with numerous exercises and examples

Group Theory In Physics: A Practitioner's Guide

Traubenberg M Rausch De,Strursberg R Campoamor
Group Theory In Physics A Practitioner s Guide Book PDF

Author : Traubenberg M Rausch De,Strursberg R Campoamor
Publisher : World Scientific
Page : 760 pages
File Size : 49,6 Mb
Release : 2018-09-19
Category : Science
ISBN : 9789813273627

Get Book

Group Theory In Physics: A Practitioner's Guide by Traubenberg M Rausch De,Strursberg R Campoamor Pdf

This book presents the study of symmetry groups in Physics from a practical perspective, i.e. emphasising the explicit methods and algorithms useful for the practitioner and profusely illustrating by examples.The first half reviews the algebraic, geometrical and topological notions underlying the theory of Lie groups, with a review of the representation theory of finite groups. The topic of Lie algebras is revisited from the perspective of realizations, useful for explicit computations within these groups. The second half is devoted to applications in physics, divided into three main parts — the first deals with space-time symmetries, the Wigner method for representations and applications to relativistic wave equations. The study of kinematical algebras and groups illustrates the properties and capabilities of the notions of contractions, central extensions and projective representations. Gauge symmetries and symmetries in Particle Physics are studied in the context of the Standard Model, finishing with a discussion on Grand-Unified Theories.

Applications of Lie Groups to Differential Equations

Peter J. Olver
Applications of Lie Groups to Differential Equations Book PDF

Author : Peter J. Olver
Publisher : Springer Science & Business Media
Page : 524 pages
File Size : 41,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781468402742

Get Book

Applications of Lie Groups to Differential Equations by Peter J. Olver Pdf

This book is devoted to explaining a wide range of applications of con tinuous symmetry groups to physically important systems of differential equations. Emphasis is placed on significant applications of group-theoretic methods, organized so that the applied reader can readily learn the basic computational techniques required for genuine physical problems. The first chapter collects together (but does not prove) those aspects of Lie group theory which are of importance to differential equations. Applications covered in the body of the book include calculation of symmetry groups of differential equations, integration of ordinary differential equations, including special techniques for Euler-Lagrange equations or Hamiltonian systems, differential invariants and construction of equations with pre scribed symmetry groups, group-invariant solutions of partial differential equations, dimensional analysis, and the connections between conservation laws and symmetry groups. Generalizations of the basic symmetry group concept, and applications to conservation laws, integrability conditions, completely integrable systems and soliton equations, and bi-Hamiltonian systems are covered in detail. The exposition is reasonably self-contained, and supplemented by numerous examples of direct physical importance, chosen from classical mechanics, fluid mechanics, elasticity and other applied areas.

Theory of Group Representations and Applications

Asim Orhan Barut,Ryszard R?czka
Theory of Group Representations and Applications Book PDF

Author : Asim Orhan Barut,Ryszard R?czka
Publisher : World Scientific
Page : 750 pages
File Size : 42,7 Mb
Release : 1986
Category : Mathematics
ISBN : 9971502178

Get Book

Theory of Group Representations and Applications by Asim Orhan Barut,Ryszard R?czka Pdf

Lie!algebras - Topological!groups - Lie!groups - Representations - Special!functions - Induced!representations.

Lie Groups, Physics, and Geometry

Robert Gilmore
Lie Groups Physics and Geometry Book PDF

Author : Robert Gilmore
Publisher : Cambridge University Press
Page : 5 pages
File Size : 40,6 Mb
Release : 2008-01-17
Category : Science
ISBN : 9781139469074

Get Book

Lie Groups, Physics, and Geometry by Robert Gilmore Pdf

Describing many of the most important aspects of Lie group theory, this book presents the subject in a 'hands on' way. Rather than concentrating on theorems and proofs, the book shows the applications of the material to physical sciences and applied mathematics. Many examples of Lie groups and Lie algebras are given throughout the text. The relation between Lie group theory and algorithms for solving ordinary differential equations is presented and shown to be analogous to the relation between Galois groups and algorithms for solving polynomial equations. Other chapters are devoted to differential geometry, relativity, electrodynamics, and the hydrogen atom. Problems are given at the end of each chapter so readers can monitor their understanding of the materials. This is a fascinating introduction to Lie groups for graduate and undergraduate students in physics, mathematics and electrical engineering, as well as researchers in these fields.

Symmetries, Lie Algebras and Representations

Jürgen Fuchs,Christoph Schweigert
Symmetries Lie Algebras and Representations Book PDF

Author : Jürgen Fuchs,Christoph Schweigert
Publisher : Cambridge University Press
Page : 464 pages
File Size : 55,5 Mb
Release : 2003-10-07
Category : Mathematics
ISBN : 0521541190

Get Book

Symmetries, Lie Algebras and Representations by Jürgen Fuchs,Christoph Schweigert Pdf

This book gives an introduction to Lie algebras and their representations. Lie algebras have many applications in mathematics and physics, and any physicist or applied mathematician must nowadays be well acquainted with them.

Symmetry, Representations, and Invariants

Roe Goodman,Nolan R. Wallach
Symmetry Representations and Invariants Book PDF

Author : Roe Goodman,Nolan R. Wallach
Publisher : Springer Science & Business Media
Page : 731 pages
File Size : 48,9 Mb
Release : 2009-07-30
Category : Mathematics
ISBN : 9780387798523

Get Book

Symmetry, Representations, and Invariants by Roe Goodman,Nolan R. Wallach Pdf

Symmetry is a key ingredient in many mathematical, physical, and biological theories. Using representation theory and invariant theory to analyze the symmetries that arise from group actions, and with strong emphasis on the geometry and basic theory of Lie groups and Lie algebras, Symmetry, Representations, and Invariants is a significant reworking of an earlier highly-acclaimed work by the authors. The result is a comprehensive introduction to Lie theory, representation theory, invariant theory, and algebraic groups, in a new presentation that is more accessible to students and includes a broader range of applications. The philosophy of the earlier book is retained, i.e., presenting the principal theorems of representation theory for the classical matrix groups as motivation for the general theory of reductive groups. The wealth of examples and discussion prepares the reader for the complete arguments now given in the general case. Key Features of Symmetry, Representations, and Invariants: (1) Early chapters suitable for honors undergraduate or beginning graduate courses, requiring only linear algebra, basic abstract algebra, and advanced calculus; (2) Applications to geometry (curvature tensors), topology (Jones polynomial via symmetry), and combinatorics (symmetric group and Young tableaux); (3) Self-contained chapters, appendices, comprehensive bibliography; (4) More than 350 exercises (most with detailed hints for solutions) further explore main concepts; (5) Serves as an excellent main text for a one-year course in Lie group theory; (6) Benefits physicists as well as mathematicians as a reference work.

Lie Groups, Lie Algebras, and Representations

Brian C. Hall
Lie Groups Lie Algebras and Representations Book PDF

Author : Brian C. Hall
Publisher : Springer Science & Business Media
Page : 376 pages
File Size : 43,5 Mb
Release : 2003-08-07
Category : Mathematics
ISBN : 0387401229

Get Book

Lie Groups, Lie Algebras, and Representations by Brian C. Hall Pdf

This book provides an introduction to Lie groups, Lie algebras, and repre sentation theory, aimed at graduate students in mathematics and physics. Although there are already several excellent books that cover many of the same topics, this book has two distinctive features that I hope will make it a useful addition to the literature. First, it treats Lie groups (not just Lie alge bras) in a way that minimizes the amount of manifold theory needed. Thus, I neither assume a prior course on differentiable manifolds nor provide a con densed such course in the beginning chapters. Second, this book provides a gentle introduction to the machinery of semi simple groups and Lie algebras by treating the representation theory of SU(2) and SU(3) in detail before going to the general case. This allows the reader to see roots, weights, and the Weyl group "in action" in simple cases before confronting the general theory. The standard books on Lie theory begin immediately with the general case: a smooth manifold that is also a group. The Lie algebra is then defined as the space of left-invariant vector fields and the exponential mapping is defined in terms of the flow along such vector fields. This approach is undoubtedly the right one in the long run, but it is rather abstract for a reader encountering such things for the first time.

The Lie Theory of Connected Pro-Lie Groups

Karl Heinrich Hofmann,Sidney A. Morris
The Lie Theory of Connected Pro Lie Groups Book PDF

Author : Karl Heinrich Hofmann,Sidney A. Morris
Publisher : European Mathematical Society
Page : 704 pages
File Size : 54,8 Mb
Release : 2007
Category : Mathematics
ISBN : 3037190329

Get Book

The Lie Theory of Connected Pro-Lie Groups by Karl Heinrich Hofmann,Sidney A. Morris Pdf

Lie groups were introduced in 1870 by the Norwegian mathematician Sophus Lie. A century later Jean Dieudonne quipped that Lie groups had moved to the center of mathematics and that one cannot undertake anything without them. If a complete topological group $G$ can be approximated by Lie groups in the sense that every identity neighborhood $U$ of $G$ contains a normal subgroup $N$ such that $G/N$ is a Lie group, then it is called a pro-Lie group. Every locally compact connected topological group and every compact group is a pro-Lie group. While the class of locally compact groups is not closed under the formation of arbitrary products, the class of pro-Lie groups is. For half a century, locally compact pro-Lie groups have drifted through the literature, yet this is the first book which systematically treats the Lie and structure theory of pro-Lie groups irrespective of local compactness. This study fits very well into the current trend which addresses infinite-dimensional Lie groups. The results of this text are based on a theory of pro-Lie algebras which parallels the structure theory of finite-dimensional real Lie algebras to an astonishing degree, even though it has had to overcome greater technical obstacles. This book exposes a Lie theory of connected pro-Lie groups (and hence of connected locally compact groups) and illuminates the manifold ways in which their structure theory reduces to that of compact groups on the one hand and of finite-dimensional Lie groups on the other. It is a continuation of the authors' fundamental monograph on the structure of compact groups (1998, 2006) and is an invaluable tool for researchers in topological groups, Lie theory, harmonic analysis, and representation theory. It is written to be accessible to advanced graduate students wishing to study this fascinating and important area of current research, which has so many fruitful interactions with other fields of mathematics.

Lie Algebras In Particle Physics

Howard Georgi
Lie Algebras In Particle Physics Book PDF

Author : Howard Georgi
Publisher : CRC Press
Page : 340 pages
File Size : 48,7 Mb
Release : 2018-05-04
Category : Science
ISBN : 9780429967764

Get Book

Lie Algebras In Particle Physics by Howard Georgi Pdf

In this book, the author convinces that Sir Arthur Stanley Eddington had things a little bit wrong, as least as far as physics is concerned. He explores the theory of groups and Lie algebras and their representations to use group representations as labor-saving tools.

Finite Groups

Bertram A. F. Wehrfritz
Finite Groups Book PDF

Author : Bertram A. F. Wehrfritz
Publisher : World Scientific
Page : 138 pages
File Size : 55,6 Mb
Release : 1999
Category : Mathematics
ISBN : 9810238746

Get Book

Finite Groups by Bertram A. F. Wehrfritz Pdf

The theory of groups, especially of finite groups, is one of the most delightful areas of mathematics. Its proofs often have elegance and crystalline beauty. This textbook is intended for the reader who has been exposed to about three years of serious mathematics. The notion of a group appears widely in mathematics and even further afield in physics and chemistry, and the fundamental idea should be known to all mathematicians. In this textbook a purely algebraic approach is taken and the choice of material is based upon the notion of conjugacy. The aim is not only to cover basic material, but also to present group theory as a living, vibrant and growing discipline, by including references and discussion of some work up to the present day.