Hexagonal Graph Paper Notebook (Composition Graph Journal Diary, #4)
by Sara Blank Book
This graduate textbook presents the basics of representation theory for finite groups from the point of view of semisimple algebras and modules over them. The presentation interweaves insights from specific examples with development of general and powerful tools based on the notion of semisimplicity. The elegant ideas of commutant duality are introduced, along with an introduction to representations of unitary groups. The text progresses systematically and the presentation is friendly and inviti...
Finite group theory is a topic remarkable for the simplicity of its statements and the difficulty of their proofs. It is used in an essential way in several branches of mathematics-for instance, in number theory. This book is a short introduction to the subject, written both for beginners and for mathematicians at large. There are ten chapters: Preliminaries, Sylow theory, Solvable groups and nilpotent groups, Group extensions, Hall subgroups, Frobenius groups, Transfer, Characters, Finite subg...
Compact Lie Groups (Graduate Texts in Mathematics, #235)
by Mark R. Sepanski
Blending algebra, analysis, and topology, the study of compact Lie groups is one of the most beautiful areas of mathematics and a key stepping stone to the theory of general Lie groups. Assuming no prior knowledge of Lie groups, this book covers the structure and representation theory of compact Lie groups. Coverage includes the construction of the Spin groups, Schur Orthogonality, the Peter-Weyl Theorem, the Plancherel Theorem, the Maximal Torus Theorem, the Commutator Theorem, the Weyl Integra...
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by Philip M. Parker
Representations and Nilpotent Orbits of Lie Algebraic Systems (Progress in Mathematics, #330)
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:P...
A solid introduction to applications of Lie groups to differential equations which have proved to be useful in practice. The computational methods are presented such that graduates and researchers can readily learn to use them. Following an exposition of the applications, the book develops the underlying theory, with many of the topics presented in a novel way, emphasising explicit examples and computations. Further examples, as well as new theoretical developments, appear in the exercises at th...
Linear Representations of Groups (Birkhauser Advanced Texts / Basler Lehrbucher, v. 2)
This book gives an exposition of the fundamentals of the theory of linear representations of finite and compact groups, as well as elements of the the- ory of linear representations of Lie groups. As an application we derive the Laplace spherical functions. The book is based on lectures that I delivered in the framework of the experimental program at the Mathematics-Mechanics Faculty of Moscow State University and at the Faculty of Professional Skill Improvement. My aim has been to give as simpl...
The work of Max Dehn (1878-1952) has been quietly influential in mathematics since the beginning of the 20th century. In 1900 he became the first to solve one of the famous Hilbert problems (the third, on the decomposition of polyhedra), in 1907 he collaborated with Heegaard to produce the first survey of topology, and in 1910 he began publishing his own investigations in topology and combinatorial group theory. His influence is apparent in the terms Dehn's algorithm, Dehn's lemma and Dehn surge...
This volume is devoted to the study of groups. Chapters 2 to 4 introduce the basic notions of groups (with operators) and their homomorphisms including presentations for groups by generators and relations. Chapter 5 considers direct and semidirect products. Chapters 6 to 8 establish Sylow theorems and study Abelian soluble and nilpotent groups. Finally chapter 9 returns to geometry and studies finite subgroups of rotations in R3. The text is rich in examples and exercises and develops the subjec...
Geometric Control of Mechanical Systems (Texts in Applied Mathematics, #49)
by Francesco Bullo and Andrew D. Lewis
The area of analysis and control of mechanical systems using differential geometry is flourishing. This book collects many results over the last decade and provides a comprehensive introduction to the area.
This book classifies the maximal subgroups of the almost simple finite classical groups in dimension up to 12; it also describes the maximal subgroups of the almost simple finite exceptional groups with socle one of Sz(q), G2(q), 2G2(q) or 3D4(q). Theoretical and computational tools are used throughout, with downloadable Magma code provided. The exposition contains a wealth of information on the structure and action of the geometric subgroups of classical groups, but the reader will also encount...
Collected Papers (Contemporary Mathematicians)
by J Nielsen and Jakob Nielsen
Infinite Dimensional Lie Algebras (Progress in Mathematics, #44)
by Victor G. Kac
This is the third, substantially revised edition of this important monograph. The book is concerned with Kac-Moody algebras, a particular class of infinite-dimensional Lie algebras, and their representations. It is based on courses given over a number of years at MIT and in Paris, and is sufficiently self-contained and detailed to be used for graduate courses. Each chapter begins with a motivating discussion and ends with a collection of exercises, with hints to the more challenging problems.
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by Philip M. Parker
Group Rings of Finite Groups Over P-Adic Integers
by Professor at Rwth Aachen Aachen W Plesken
This book is appropriate for second to fourth year undergraduates. In addition to the material traditionally taught at this level, the book contains several applications: Polya-Burnside Enumeration, Mutually Orthogonal Latin Squares, Error-Correcting Codes and a classification of the finite groups of isometries of the plane and the finite rotation groups in Euclidean 3-space. It is hoped that these applications will help the reader achieve a better grasp of the rather abstract ideas presented an...
60 Worksheets - Less Than for 3 Digit Numbers (60 Days Math Less Than, #3)
by Kapoo Stem
Given a mathematical structure, one of the basic associated mathematical objects is its automorphism group. The object of this book is to give a biased account of automorphism groups of differential geometric struc tures. All geometric structures are not created equal; some are creations of ~ods while others are products of lesser human minds. Amongst the former, Riemannian and complex structures stand out for their beauty and wealth. A major portion of this book is therefore devoted to these t...
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by Philip M. Parker
Geometry and Cohomology in Group Theory (London Mathematical Society Lecture Note)
This volume reflects the fruitful connections between group theory and topology. It contains articles on cohomology, representation theory, geometric and combinatorial group theory. Some of the world's best known figures in this very active area of mathematics have made contributions, including substantial articles from Ol'shanskii, Mikhajlovskii, Carlson, Benson, Linnell, Wilson and Grigorchuk, which will be valuable reference works for some years to come. Pure mathematicians working in the fie...