Books in Topological groups lie groups

Introduction to Finite and Infinite Dimensional Lie (Super)algebras

1st Edition
April 4, 2016
Neelacanta Sthanumoorthy
English
Hardback
9 7 8 0 1 2 8 0 4 6 7 5 3
eBook
9 7 8 0 1 2 8 0 4 6 8 3 8

Lie superalgebras are a natural generalization of Lie algebras, having applications in geometry, number theory, gauge field theory, and string theory. Introduction to Finite and Infinite Dimensional Lie Algebras and Superalgebras introduces the theory of Lie superalgebras, their algebras, and their representations. The material covered ranges from basic definitions of Lie groups to the classification of finite-dimensional representations of semi-simple Lie algebras. While discussing all classes of finite and infinite dimensional Lie algebras and Lie superalgebras in terms of their different classes of root systems, the book focuses on Kac-Moody algebras. With numerous exercises and worked examples, it is ideal for graduate courses on Lie groups and Lie algebras.

Explorations in Topology

2nd Edition
December 4, 2013
David Gay
English
eBook
9 7 8 0 1 2 4 1 6 6 4 0 0

Explorations in Topology, Second Edition, provides students a rich experience with low-dimensional topology (map coloring, surfaces, and knots), enhances their geometrical and topological intuition, empowers them with new approaches to solving problems, and provides them with experiences that will help them make sense of future, more formal topology courses. The book's innovative story-line style models the problem-solving process, presents the development of concepts in a natural way, and engages students in meaningful encounters with the material. The updated end-of-chapter investigations provide opportunities to work on many open-ended, non-routine problems and, through a modified "Moore method," to make conjectures from which theorems emerge. The revised end-of-chapter notes provide historical background to the chapter's ideas, introduce standard terminology, and make connections with mainstream mathematics. The final chapter of projects provides ideas for continued research. Explorations in Topology, Second Edition, enhances upper division courses and is a valuable reference for all levels of students and researchers working in topology.

Supersymmetries and Infinite-Dimensional Algebras

1st Edition
Volume 3
October 22, 2013
N. H. March
English
eBook
9 7 8 1 4 8 3 2 8 8 3 7 6

Recent devopments, particularly in high-energy physics, have projected group theory and symmetry consideration into a central position in theoretical physics. These developments have taken physicists increasingly deeper into the fascinating world of pure mathematics. This work presents important mathematical developments of the last fifteen years in a form that is easy to comprehend and appreciate.

Lie Algebras: Theory and Algorithms

1st Edition
Volume 56
February 4, 2000
W.A. de Graaf
English
eBook
9 7 8 0 0 8 0 5 3 5 4 5 6

The aim of the present work is two-fold. Firstly it aims at a giving an account of many existing algorithms for calculating with finite-dimensional Lie algebras. Secondly, the book provides an introduction into the theory of finite-dimensional Lie algebras. These two subject areas are intimately related. First of all, the algorithmic perspective often invites a different approach to the theoretical material than the one taken in various other monographs (e.g., [42], [48], [77], [86]). Indeed, on various occasions the knowledge of certain algorithms allows us to obtain a straightforward proof of theoretical results (we mention the proof of the Poincaré-Birkhoff-Witt theorem and the proof of Iwasawa's theorem as examples). Also proofs that contain algorithmic constructions are explicitly formulated as algorithms (an example is the isomorphism theorem for semisimple Lie algebras that constructs an isomorphism in case it exists). Secondly, the algorithms can be used to arrive at a better understanding of the theory. Performing the algorithms in concrete examples, calculating with the concepts involved, really brings the theory of life.

Lie Algebras, Part 2

1st Edition
Volume 7
October 30, 1997
E.A. de Kerf + 2 more
English
eBook
9 7 8 0 0 8 0 5 3 5 4 6 3

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.

Continuous Linear Representations

1st Edition
Volume 168
January 30, 1992
Z. Magyar
English
eBook
9 7 8 0 0 8 0 8 7 2 7 9 7

This monograph gives access to the theory of continuous linear representations of general real Lie groups to readers who are already familiar with the rudiments of functional analysis and Lie groups. The first half of the book is centered around the relation between a continuous linear representation (of a Lie group over a Banach space or even a more general space) and its tangent; the latter is a Lie algebra representation in a sense. Starting with the Hille-Yosida theory, quite recent results are reached. The second half is more standard unitary theory with applications concerning the Galilean and Poincaré groups. Appendices help readers with diverse backgrounds to find the precise descriptions of the concepts needed from earlier literature.Each chapter includes exercises.

Topological Fields

1st Edition
Volume 157
June 1, 1989
S. Warner
English
eBook
9 7 8 0 0 8 0 8 7 2 6 8 1

Aimed at those acquainted with basic point-set topology and algebra, this text goes up to the frontiers of current research in topological fields (more precisely, topological rings that algebraically are fields).The reader is given enough background to tackle the current literature without undue additional preparation. Many results not in the text (and many illustrations by example of theorems in the text) are included among the exercises. Sufficient hints for the solution of the exercises are offered so that solving them does not become a major research effort for the reader. A comprehensive bibliography completes the volume.

Representations of -Algebras, Locally Compact Groups, and Banach -Algebraic Bundles

1st Edition
Volume 2
April 28, 1988
J. M.G. Fell + 1 more
English
Hardback
9 7 8 0 1 2 2 5 2 7 2 2 7
eBook
9 7 8 0 0 8 0 8 7 4 4 5 6

This is an all-encompassing and exhaustive exposition of the theory of infinite-dimensional Unitary Representations of Locally Compact Groups and its generalization to representations of Banach algebras. The presentation is detailed, accessible, and self-contained (except for some elementary knowledge in algebra, topology, and abstract measure theory). In the later chapters the reader is brought to the frontiers of present-day knowledge in the area of Mackey normal subgroup analysisand its generalization to the context of Banach *-Algebraic Bundles.

Representations of -Algebras, Locally Compact Groups, and Banach -Algebraic Bundles

1st Edition
Volume 1
March 28, 1988
J. M.G. Fell + 1 more
English
Hardback
9 7 8 0 1 2 2 5 2 7 2 1 0
eBook
9 7 8 0 0 8 0 8 7 4 4 4 9

Spaces of Fundamental and Generalized Functions

1st Edition
January 1, 1968
I. M. Gel'Fand + 1 more
English
eBook
9 7 8 1 4 8 3 2 6 2 3 0 7

Spaces of Fundamental and Generalized Functions, Volume 2, analyzes the general theory of linear topological spaces. The basis of the theory of generalized functions is the theory of the so-called countably normed spaces (with compatible norms), their unions (inductive limits), and also of the spaces conjugate to the countably normed ones or their unions. This set of spaces is sufficiently broad on the one hand, and sufficiently convenient for the analyst on the other. The book opens with a chapter that discusses the theory of these spaces. This is followed by separate chapters on fundamental and generalized functions, Fourier transformations of fundamental and generalized functions, and spaces of type S.

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Books in Topological groups lie groups

Introduction to Finite and Infinite Dimensional Lie (Super)algebras

Explorations in Topology

Supersymmetries and Infinite-Dimensional Algebras

Lie Algebras: Theory and Algorithms

Lie Algebras, Part 2

Continuous Linear Representations

Topological Fields

Representations of -Algebras, Locally Compact Groups, and Banach -Algebraic Bundles

Representations of -Algebras, Locally Compact Groups, and Banach -Algebraic Bundles

Spaces of Fundamental and Generalized Functions