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Group Theory

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Lie Groups (18)

e-books in Group Theory category

Book cover: An Introduction to the Theory of Groups of Finite OrderAn Introduction to the Theory of Groups of Finite Order
by - Oxford Clarendon Press ,
This book aims at introducing the reader to more advanced treatises and original papers on Groups of finite order. The subject requires for its study only an elementary knowledge of Algebra. I have tried to lighten for him the initial difficulties.
(846 views)
Book cover: Thin Groups and Superstrong ApproximationThin Groups and Superstrong Approximation
by - Cambridge University Press ,
This book focuses on recent developments concerning various quantitative aspects of thin groups. It provides a broad panorama of a very active field of mathematics at the boundary between geometry, dynamical systems, number theory, and combinatorics.
(1179 views)

Book cover: Groups and Semigroups: Connections and ContrastsGroups and Semigroups: Connections and Contrasts
by - University of Nebraska-Lincoln ,
In the present paper, I will discuss some of these connections between group theory and semigroup theory, and I will also discuss some rather surprising contrasts between the theories. I will focus primarily on the theory of inverse semigroups.
(4033 views)
Book cover: Theory and Applications of Finite GroupsTheory and Applications of Finite Groups
by - J. Wiley ,
The book presents in a unified manner the more fundamental aspects of finite groups and their applications, and at the same time preserves the advantage which arises when each branch of an extensive subject is written by a specialist in that branch.
(2650 views)
Book cover: An Introduction to Group Theory: Applications to Mathematical Music TheoryAn Introduction to Group Theory: Applications to Mathematical Music Theory
by - BookBoon ,
In this text, a modern presentation of the fundamental notions of Group Theory is chosen, where the language of commutative diagrams and universal properties, so necessary in Modern Mathematics, in Physics and Computer Science, is introduced.
(5113 views)
Book cover: Theory of Groups of Finite OrderTheory of Groups of Finite Order
by - Cambridge University Press ,
After introducing permutation notation and defining group, the author discusses the simpler properties of group that are independent of their modes of representation; composition-series of groups; isomorphism of a group with itself; etc.
(4712 views)
Book cover: Frobenius Splittings and B-ModulesFrobenius Splittings and B-Modules
by - Springer ,
The course given by the author in 1992 explains the solution by O. Mathieu of some conjectures in the representation theory of arbitrary semisimple algebraic groups. The conjectures concern filtrations of 'standard' representations.
(3978 views)
Book cover: Congruence Lattices of Finite AlgebrasCongruence Lattices of Finite Algebras
by - arXiv ,
We review a number of methods for finding a finite algebra with a given congruence lattice, including searching for intervals in subgroup lattices. We also consider methods for proving that algebras with a given congruence lattice exist...
(4087 views)
Book cover: Lectures on Topics In The Theory of Infinite GroupsLectures on Topics In The Theory of Infinite Groups
by - Tata Institute of Fundamental Research ,
As the title suggests, the aim was not a systematic treatment of infinite groups. Instead the author tried to present some of the methods and results that are new and look promising, and that have not yet found their way into the books.
(4434 views)
Book cover: Finite Group SchemesFinite Group Schemes
by - ETH Zurich ,
The aim of the lecture course is the classification of finite commutative group schemes over a perfect field of characteristic p, using the classical approach by contravariant Dieudonne theory. The theory is developed from scratch.
(4591 views)
Book cover: Galois Groups and Fundamental GroupsGalois Groups and Fundamental Groups
by - San Francisco State University ,
This course brings together two areas of mathematics that each concern symmetry -- symmetry in algebra, in the case of Galois theory; and symmetry in geometry, in the case of fundamental groups. Prerequisites are courses in algebra and analysis.
(5091 views)
Book cover: Representation Theory of Compact GroupsRepresentation Theory of Compact Groups
by - Aalto TKK ,
Contents: Groups (Groups without topology, Group actions and representations); Topological groups (Compact groups, Haar measure, Fourier transforms on compact groups..); Linear Lie groups (Exponential map, Lie groups and Lie algebras); Hopf algebras.
(5809 views)
Book cover: Lectures on Algebraic GroupsLectures on Algebraic Groups
by - University of Oregon ,
Contents: General Algebra; Commutative Algebra; Affine and Projective Algebraic Sets; Varieties; Morphisms; Tangent spaces; Complete Varieties; Basic Concepts; Lie algebra of an algebraic group; Quotients; Semisimple and unipotent elements; etc.
(6165 views)
Book cover: Geometry and Group TheoryGeometry and Group Theory
by - Texas A&M University ,
Lecture notes on Geometry and Group Theory. In this course, we develop the basic notions of Manifolds and Geometry, with applications in physics, and also we develop the basic notions of the theory of Lie Groups, and their applications in physics.
(11509 views)
Book cover: Elements of Group TheoryElements of Group Theory
by - arXiv ,
The following notes are the basis for a graduate course. They are oriented towards the application of group theory to particle physics, although some of it can be used for general quantum mechanics. They have no pretense of mathematical rigor.
(9564 views)
Book cover: Interval GroupoidsInterval Groupoids
by - arXiv ,
This book defines new classes of groupoids, like matrix groupoid, polynomial groupoid, interval groupoid, and polynomial groupoid. This book introduces 77 new definitions substantiated and described by 426 examples and 150 theorems.
(4464 views)
Book cover: Finite Rank Torsion Free Modules Over Dedekind DomainsFinite Rank Torsion Free Modules Over Dedekind Domains
by - University of Hawaii ,
Contents: Modules Over Commutative Rings; Fundamentals; Rank-one Modules and Types; Quasi-Homomorphisms; The t-Socle and t-Radical; Butler Modules; Splitting Rings and Splitting Fields; Torsion Free Rings; Quotient Divisible Modules; etc.
(4361 views)
Book cover: Lie groups and Lie algebrasLie groups and Lie algebras
by - UC Berkeley ,
From the table of contents: Tangent Lie algebras to Lie groups; Simply Connected Lie Groups; Hopf Algebras; PBW Theorem and Deformations; Lie algebra cohomology; Engel's Theorem and Lie's Theorem; Cartan Criterion, Whitehead and Weyl Theorems; etc.
(6430 views)
Book cover: Why are Braids Orderable?Why are Braids Orderable?
by ,
This book is an account of several quite different approaches to Artin's braid groups, involving self-distributive algebra, uniform finite trees, combinatorial group theory, mapping class groups, laminations, and hyperbolic geometry.
(6866 views)
Book cover: Introduction to Lie Groups and Lie AlgebrasIntroduction to Lie Groups and Lie Algebras
by - SUNY at Stony Brook ,
The book covers the basic contemporary theory of Lie groups and Lie algebras. This classic graduate text focuses on the study of semisimple Lie algebras, developing the necessary theory along the way. Written in an informal style.
(8481 views)
Book cover: Algebraic Groups, Lie Groups, and their Arithmetic SubgroupsAlgebraic Groups, Lie Groups, and their Arithmetic Subgroups
by ,
This work is a modern exposition of the theory of algebraic group schemes, Lie groups, and their arithmetic subgroups. Algebraic groups are groups defined by polynomials. Those in this book can all be realized as groups of matrices.
(6606 views)
Book cover: Introduction to Arithmetic GroupsIntroduction to Arithmetic Groups
by - arXiv ,
This revised version of a book in progress on arithmetic groups and locally symmetric spaces contains several additional chapters, including the proofs of three major theorems of G. A. Margulis (superrigidity, arithmeticity, and normal subgroups).
(5321 views)
Book cover: Smarandache SemigroupsSmarandache Semigroups
by - American Research Press ,
The Smarandache semigroups exhibit properties of both a group and a semigroup simultaneously. This book assumes the reader to have a good background on group theory; we give some recollection about groups and some of its properties for reference.
(4894 views)
Book cover: Groupoids and Smarandache GroupoidsGroupoids and Smarandache Groupoids
by - American Research Press ,
This book by Dr. W. B. Vasantha aims to give a systematic development of the basic non-associative algebraic structures viz. Smarandache groupoids. Smarandache groupoids exhibits simultaneously the properties of a semigroup and a groupoid.
(5164 views)
Book cover: Group TheoryGroup Theory
by ,
Contents: Basic Definitions and Results; Free Groups and Presentations; Coxeter Groups; Automorphisms and Extensions; Groups Acting on Sets; The Sylow Theorems; Subnormal Series; Solvable and Nilpotent Groups; Representations of Finite Groups.
(7462 views)
Book cover: Groups as GraphsGroups as Graphs
by - CuArt ,
In this book, for the first time, the authors represented every finite group in the form of a graph. This study is significant because properties of groups can be immediately obtained by looking at the graphs of the groups.
(6331 views)
Book cover: Galois Groups and Fundamental GroupsGalois Groups and Fundamental Groups
by - Cambridge University Press ,
This book contains eight articles which focus on presenting recently developed new aspects of the theory of Galois groups and fundamental groups, avoiding classical aspects which have already been developed at length in the standard literature.
(7947 views)
Book cover: Groups: Presentations and RepresentationsGroups: Presentations and Representations
by - Macquarie University ,
This is a first course on group theory suitable to a third year student. It motivates group theory with many illustrative examples such as shuffling of cards and permutation puzzles. There's an elementary introduction to representation theory.
(8567 views)
Book cover: Group theory for Maths, Physics and ChemistryGroup theory for Maths, Physics and Chemistry
by ,
Symmetry plays an important role in chemistry and physics. Group captures the symmetry in a very efficient manner. We focus on abstract group theory, deal with representations of groups, and deal with some applications in chemistry and physics.
(8215 views)
Book cover: Group TheoryGroup Theory
by - University of Lund ,
The text deals with basic Group Theory and its applications. Contents: Abstract Group Theory; Theory of Group Representations; Group Theory in Quantum Mechanics; Lie Groups; Atomic Physics; The Group SU2: Isospin; The Point Groups; The Group SU3.
(8289 views)
Book cover: Symmetry Groups and Their ApplicationsSymmetry Groups and Their Applications
by - Academic Press ,
A beginning graduate level book on applied group theory. Only those aspects of group theory are treated which are useful in the physical sciences, but the mathematical apparatus underlying the applications is presented with a high degree of rigor.
(8310 views)
Book cover: An Elementary Introduction to Groups and RepresentationsAn Elementary Introduction to Groups and Representations
by - arXiv ,
An elementary introduction to Lie groups, Lie algebras, and their representations. Topics include definitions and examples of Lie groups and Lie algebras, the basics of representations theory, the Baker-Campbell-Hausdorff formula, and more.
(12206 views)
Book cover: Notes on Categories and GroupoidsNotes on Categories and Groupoids
by - Van Nostrand Reinhold ,
A self-contained account of the elementary theory of groupoids and some of its uses in group theory and topology. Category theory appears as a secondary topic whenever it is relevant to the main issue, and its treatment is by no means systematic.
(8898 views)
Book cover: Combinatorial Group TheoryCombinatorial Group Theory
by - University of Melbourne ,
Lecture notes for the subject Combinatorial Group Theory at the University of Melbourne. Contents: About groups; Free groups and presentations; Construction of new groups; Properties, embeddings and examples; Subgroup Theory; Decision Problems.
(8339 views)
Book cover: Group Characters, Symmetric Functions, and the Hecke AlgebraGroup Characters, Symmetric Functions, and the Hecke Algebra
by - American Mathematical Society ,
The book covers a set of interrelated topics, presenting a self-contained exposition of the algebra behind the Jones polynomial along with various excursions into related areas. Directed at graduate students and mathematicians.
(6522 views)
Book cover: Introduction to Groups, Invariants and ParticlesIntroduction to Groups, Invariants and Particles
by - Orange Grove Texts Plus ,
This is an introduction to group theory, with an emphasis on Lie groups and their application to the study of symmetries of the fundamental constituents of matter. The text was written for seniors and advanced juniors, majoring in the physical sciences.
(12656 views)
Book cover: Group Theory: Birdtracks, Lie's, and Exceptional GroupsGroup Theory: Birdtracks, Lie's, and Exceptional Groups
by - Princeton University Press ,
A book on the theory of Lie groups for researchers and graduate students in theoretical physics and mathematics. It answers what Lie groups preserve trilinear, quadrilinear, and higher order invariants. Written in a lively and personable style.
(9182 views)