Algebras Representations And Applications
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Author |
: Asim Orhan Barut |
Publisher |
: World Scientific |
Total Pages |
: 750 |
Release |
: 1986 |
ISBN-10 |
: 9971502178 |
ISBN-13 |
: 9789971502171 |
Rating |
: 4/5 (78 Downloads) |
Synopsis Theory of Group Representations and Applications by : Asim Orhan Barut
Lie!algebras - Topological!groups - Lie!groups - Representations - Special!functions - Induced!representations.
Author |
: Alexander Zimmermann |
Publisher |
: Springer |
Total Pages |
: 720 |
Release |
: 2014-08-15 |
ISBN-10 |
: 9783319079684 |
ISBN-13 |
: 3319079689 |
Rating |
: 4/5 (84 Downloads) |
Synopsis Representation Theory by : Alexander Zimmermann
Introducing the representation theory of groups and finite dimensional algebras, first studying basic non-commutative ring theory, this book covers the necessary background on elementary homological algebra and representations of groups up to block theory. It further discusses vertices, defect groups, Green and Brauer correspondences and Clifford theory. Whenever possible the statements are presented in a general setting for more general algebras, such as symmetric finite dimensional algebras over a field. Then, abelian and derived categories are introduced in detail and are used to explain stable module categories, as well as derived categories and their main invariants and links between them. Group theoretical applications of these theories are given – such as the structure of blocks of cyclic defect groups – whenever appropriate. Overall, many methods from the representation theory of algebras are introduced. Representation Theory assumes only the most basic knowledge of linear algebra, groups, rings and fields and guides the reader in the use of categorical equivalences in the representation theory of groups and algebras. As the book is based on lectures, it will be accessible to any graduate student in algebra and can be used for self-study as well as for classroom use.
Author |
: James Lepowsky |
Publisher |
: Springer Science & Business Media |
Total Pages |
: 330 |
Release |
: 2012-12-06 |
ISBN-10 |
: 9780817681869 |
ISBN-13 |
: 0817681868 |
Rating |
: 4/5 (69 Downloads) |
Synopsis Introduction to Vertex Operator Algebras and Their Representations by : James Lepowsky
* Introduces the fundamental theory of vertex operator algebras and its basic techniques and examples. * Begins with a detailed presentation of the theoretical foundations and proceeds to a range of applications. * Includes a number of new, original results and brings fresh perspective to important works of many other researchers in algebra, lie theory, representation theory, string theory, quantum field theory, and other areas of math and physics.
Author |
: Robert N. Cahn |
Publisher |
: Courier Corporation |
Total Pages |
: 180 |
Release |
: 2014-06-10 |
ISBN-10 |
: 9780486150314 |
ISBN-13 |
: 0486150313 |
Rating |
: 4/5 (14 Downloads) |
Synopsis Semi-Simple Lie Algebras and Their Representations by : Robert N. Cahn
Designed to acquaint students of particle physiME already familiar with SU(2) and SU(3) with techniques applicable to all simple Lie algebras, this text is especially suited to the study of grand unification theories. Author Robert N. Cahn, who is affiliated with the Lawrence Berkeley National Laboratory in Berkeley, California, has provided a new preface for this edition. Subjects include the killing form, the structure of simple Lie algebras and their representations, simple roots and the Cartan matrix, the classical Lie algebras, and the exceptional Lie algebras. Additional topiME include Casimir operators and Freudenthal's formula, the Weyl group, Weyl's dimension formula, reducing product representations, subalgebras, and branching rules. 1984 edition.
Author |
: Francesco Iachello |
Publisher |
: Springer |
Total Pages |
: 208 |
Release |
: 2007-02-22 |
ISBN-10 |
: 9783540362395 |
ISBN-13 |
: 3540362398 |
Rating |
: 4/5 (95 Downloads) |
Synopsis Lie Algebras and Applications by : Francesco Iachello
This book, designed for advanced graduate students and post-graduate researchers, introduces Lie algebras and some of their applications to the spectroscopy of molecules, atoms, nuclei and hadrons. The book contains many examples that help to elucidate the abstract algebraic definitions. It provides a summary of many formulas of practical interest, such as the eigenvalues of Casimir operators and the dimensions of the representations of all classical Lie algebras.
Author |
: Alexey P Isaev |
Publisher |
: World Scientific |
Total Pages |
: 615 |
Release |
: 2020-07-16 |
ISBN-10 |
: 9789811217425 |
ISBN-13 |
: 9811217424 |
Rating |
: 4/5 (25 Downloads) |
Synopsis Theory Of Groups And Symmetries: Representations Of Groups And Lie Algebras, Applications by : Alexey P Isaev
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.
Author |
: Roe Goodman |
Publisher |
: Cambridge University Press |
Total Pages |
: 708 |
Release |
: 2000-01-13 |
ISBN-10 |
: 0521663482 |
ISBN-13 |
: 9780521663489 |
Rating |
: 4/5 (82 Downloads) |
Synopsis Representations and Invariants of the Classical Groups by : Roe Goodman
More than half a century has passed since Weyl's 'The Classical Groups' gave a unified picture of invariant theory. This book presents an updated version of this theory together with many of the important recent developments. As a text for those new to the area, this book provides an introduction to the structure and finite-dimensional representation theory of the complex classical groups that requires only an abstract algebra course as a prerequisite. The more advanced reader will find an introduction to the structure and representations of complex reductive algebraic groups and their compact real forms. This book will also serve as a reference for the main results on tensor and polynomial invariants and the finite-dimensional representation theory of the classical groups. It will appeal to researchers in mathematics, statistics, physics and chemistry whose work involves symmetry groups, representation theory, invariant theory and algebraic group theory.
Author |
: Daniel Simson |
Publisher |
: CRC Press |
Total Pages |
: 516 |
Release |
: 1993-01-01 |
ISBN-10 |
: 2881248284 |
ISBN-13 |
: 9782881248283 |
Rating |
: 4/5 (84 Downloads) |
Synopsis Linear Representations of Partially Ordered Sets and Vector Space Categories by : Daniel Simson
This volume provides an elementary yet comprehensive introduction to representations of partially ordered sets and bimodule matrix problems, and their use in representation theory of algebras. It includes a discussion of representation types of algebras and partially ordered sets. Various characterizations of representation-finite and representation-tame partially ordered sets are offered and a description of their indecomposable representations is given. Auslander-Reiten theory is demonstrated together with a computer accessible algorithm for determining in decomposable representations and the Auslander-Reiten quiver of any representation-finite partially ordered set.
Author |
: Peter J. Olver |
Publisher |
: Springer Science & Business Media |
Total Pages |
: 524 |
Release |
: 2012-12-06 |
ISBN-10 |
: 9781468402742 |
ISBN-13 |
: 1468402749 |
Rating |
: 4/5 (42 Downloads) |
Synopsis Applications of Lie Groups to Differential Equations by : Peter J. Olver
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.
Author |
: Celine Carstensen-Opitz |
Publisher |
: Walter de Gruyter GmbH & Co KG |
Total Pages |
: 422 |
Release |
: 2019-09-02 |
ISBN-10 |
: 9783110603996 |
ISBN-13 |
: 3110603993 |
Rating |
: 4/5 (96 Downloads) |
Synopsis Abstract Algebra by : Celine Carstensen-Opitz
A new approach to conveying abstract algebra, the area that studies algebraic structures, such as groups, rings, fields, modules, vector spaces, and algebras, that is essential to various scientific disciplines such as particle physics and cryptology. It provides a well written account of the theoretical foundations and it also includes a chapter on cryptography. End of chapter problems help readers with accessing the subjects.