Space Groups and Their Representations
Author: George F. Koster
Publisher:
Published: 1964
Total Pages: 84
ISBN-13:
DOWNLOAD EBOOKPosts
The Mathematical Theory of Symmetry in Solids
Author: Christopher Bradley
Publisher: Oxford University Press
Published: 2010
Total Pages: 758
ISBN-13: 0199582580
DOWNLOAD EBOOKThis classic book gives, in extensive tables, the irreducible representations of the crystallographic point groups and space groups. These are useful in studying the eigenvalues and eigenfunctions of a particle or quasi-particle in a crystalline solid. The theory is extended to the corepresentations of the Shubnikov groups.
Group Theory
Author: Mildred S. Dresselhaus
Publisher: Springer Science & Business Media
Published: 2007-12-18
Total Pages: 576
ISBN-13: 3540328998
DOWNLOAD EBOOKThis concise, class-tested book was refined over the authors’ 30 years as instructors at MIT and the University Federal of Minas Gerais (UFMG) in Brazil. The approach centers on the conviction that teaching group theory along with applications helps students to learn, understand and use it for their own needs. Thus, the theoretical background is confined to introductory chapters. Subsequent chapters develop new theory alongside applications so that students can retain new concepts, build on concepts already learned, and see interrelations between topics. Essential problem sets between chapters aid retention of new material and consolidate material learned in previous chapters.
A Course in Finite Group Representation Theory
Author: Peter Webb
Publisher: Cambridge University Press
Published: 2016-08-19
Total Pages: 339
ISBN-13: 1107162394
DOWNLOAD EBOOKThis graduate-level text provides a thorough grounding in the representation theory of finite groups over fields and rings. The book provides a balanced and comprehensive account of the subject, detailing the methods needed to analyze representations that arise in many areas of mathematics. Key topics include the construction and use of character tables, the role of induction and restriction, projective and simple modules for group algebras, indecomposable representations, Brauer characters, and block theory. This classroom-tested text provides motivation through a large number of worked examples, with exercises at the end of each chapter that test the reader's knowledge, provide further examples and practice, and include results not proven in the text. Prerequisites include a graduate course in abstract algebra, and familiarity with the properties of groups, rings, field extensions, and linear algebra.
Introduction to the Theory of Banach Representations of Groups
Author: Yurii I. Lyubich
Publisher: Birkhäuser
Published: 2012-12-06
Total Pages: 231
ISBN-13: 3034891695
DOWNLOAD EBOOKThe theory of group representations plays an important roie in modern mathematics and its applica~ions to natural sciences. In the compulsory university curriculum it is included as a branch of algebra, dealing with representations of finite groups (see, for example, the textbook of A. I. Kostrikin [25]). The representation theory for compact, locally compact Abelian, and Lie groups is co vered in graduate courses, concentrated around functional analysis. The author of the present boo~ has lectured for many years on functional analysis at Khar'kov University. He subsequently con tinued these lectures in the form of a graduate course on the theory of group representations, in which special attention was devoted to a retrospective exposition of operator theory and harmo nic analysis of functions from the standpoint of representation theory. In this approach it was natural to consider not only uni tary, but also Banach representations, and not only representations of groups, but also of semigroups.
Irreducible Representations of the Space Groups
Author: Oleg Vladimirovich Kovalev
Publisher: Routledge
Published: 1965
Total Pages: 176
ISBN-13:
DOWNLOAD EBOOKRepresentation Theory
Author: William Fulton
Publisher: Springer Science & Business Media
Published: 1991
Total Pages: 616
ISBN-13: 9780387974958
DOWNLOAD EBOOKIntroducing finite-dimensional representations of Lie groups and Lie algebras, this example-oriented book works from representation theory of finite groups, through Lie groups and Lie algrbras to the finite dimensional representations of the classical groups.
Group Representation Theory For Physicists (2nd Edition)
Author: Jialun Ping
Publisher: World Scientific Publishing Company
Published: 2002-08-15
Total Pages: 602
ISBN-13: 981310600X
DOWNLOAD EBOOKThis book introduces systematically the eigenfunction method, a new approach to the group representation theory which was developed by the authors in the 1970's and 1980's in accordance with the concept and method used in quantum mechanics. It covers the applications of the group theory in various branches of physics and quantum chemistry, especially nuclear and molecular physics. Extensive tables and computational methods are presented.Group Representation Theory for Physicists may serve as a handbook for researchers doing group theory calculations. It is also a good reference book and textbook for undergraduate and graduate students who intend to use group theory in their future research careers.
Modular Representation Theory of Finite Groups
Author: Peter Schneider
Publisher: Springer Science & Business Media
Published: 2012-11-27
Total Pages: 183
ISBN-13: 1447148320
DOWNLOAD EBOOKRepresentation theory studies maps from groups into the general linear group of a finite-dimensional vector space. For finite groups the theory comes in two distinct flavours. In the 'semisimple case' (for example over the field of complex numbers) one can use character theory to completely understand the representations. This by far is not sufficient when the characteristic of the field divides the order of the group. Modular Representation Theory of finite Groups comprises this second situation. Many additional tools are needed for this case. To mention some, there is the systematic use of Grothendieck groups leading to the Cartan matrix and the decomposition matrix of the group as well as Green's direct analysis of indecomposable representations. There is also the strategy of writing the category of all representations as the direct product of certain subcategories, the so-called 'blocks' of the group. Brauer's work then establishes correspondences between the blocks of the original group and blocks of certain subgroups the philosophy being that one is thereby reduced to a simpler situation. In particular, one can measure how nonsemisimple a category a block is by the size and structure of its so-called 'defect group'. All these concepts are made explicit for the example of the special linear group of two-by-two matrices over a finite prime field. Although the presentation is strongly biased towards the module theoretic point of view an attempt is made to strike a certain balance by also showing the reader the group theoretic approach. In particular, in the case of defect groups a detailed proof of the equivalence of the two approaches is given. This book aims to familiarize students at the masters level with the basic results, tools, and techniques of a beautiful and important algebraic theory. Some basic algebra together with the semisimple case are assumed to be known, although all facts to be used are restated (without proofs) in the text. Otherwise the book is entirely self-contained.
Representations of Algebraic Groups
Author: Jens Carsten Jantzen
Publisher: American Mathematical Soc.
Published: 2003
Total Pages: 594
ISBN-13: 082184377X
DOWNLOAD EBOOKGives an introduction to the general theory of representations of algebraic group schemes. This title deals with representation theory of reductive algebraic groups and includes topics such as the description of simple modules, vanishing theorems, Borel-Bott-Weil theorem and Weyl's character formula, and Schubert schemes and lne bundles on them.
