مقدمه‌ای بر نظریه نمایش (کتابخانه ریاضی دانشجویی، جلد ۵۹)

Very Roughly Speaking, Representation Theory Studies Symmetry In Linear Spaces. It Is A Beautiful Mathematical Subject Which Has Many Applications, Ranging From Number Theory And Combinatorics To Geometry, Probability Theory, Quantum Mechanics, And Quantum Field Theory. The Goal Of This Book Is To Give A Holistic Introduction To Representation Theory, Presenting It As A Unified Subject Which Studies Representations Of Associative Algebras And Treating The Representation Theories Of Groups, Lie Algebras, And Quivers As Special Cases. Using This Approach, The Book Covers A Number Of Standard Topics In The Representation Theories Of These Structures. Theoretical Material In The Book Is Supplemented By Many Problems And Exercises Which Touch Upon A Lot Of Additional Topics; The More Difficult Exercises Are Provided With Hints. The Book Is Designed As A Textbook For Advanced Undergraduate And Beginning Graduate Students. It Should Be Accessible To Students With A Strong Background In Linear Algebra And A Basic Knowledge Of Abstract Algebra.--page 4 Of Cover. Introduction -- Basic Notions Of Representation Theory -- General Results Of Representation Theory -- Representations Of Finite Groups: Basic Results -- Representations Of Finite Groups: Further Results -- Quiver Representations -- Introduction To Categories -- Homological Algebra. Pavel Etingof ... [et Al.] ; With Historical Interludes By Slava Gerovitch. Includes Bibliographical References (p. 217-221) And Index. Representation theory studies symmetry in linear spaces and this introduction is for graduate and advanced undergraduate students of mathematics who have a solid foundation in linear algebra and at least a smattering of abstract algebra. It covers basic notions, general results, representations of finite groups, quiver representations, categories, homological algebra, and the structure of finite dimensional algebras. Annotation 2011 Book News, Inc., Portland, OR (booknews.com)