Lie Groups, Lie Algebras, and Cohomology
By (author) Anthony W. Knapp
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Lie Groups, Lie Algebras, and Cohomology by Anthony W. Knapp
Book DescriptionThis book starts with the elementary theory of Lie groups of matrices and arrives at the definition, elementary properties, and first applications of cohomological induction, which is a recently discovered algebraic construction of group representations. Along the way it develops the computational techniques that are so important in handling Lie groups. The book is based on a one-semester course given at the State University of New York, Stony Brook in fall, 1986 to an audience having little or no background in Lie groups but interested in seeing connections among algebra, geometry, and Lie theory. These notes develop what is needed beyond a first graduate course in algebra in order to appreciate cohomological induction and to see its first consequences. Along the way one is able to study homological algebra with a significant application in mind; consequently one sees just what results in that subject are fundamental and what results are minor.
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Book DetailsISBN: 9780691084985
(235mm x 155mm x 31mm)
Imprint: Princeton University Press
Publisher: Princeton University Press
Publish Date: 1-May-1988
Country of Publication: United States
Books By Author Anthony W. Knapp
Advanced Algebra, Hardback (November 2007)
Basic Algebra and Advanced Algebra systematically develop concepts and tools in algebra that are vital to every mathematician, whether pure or applied, aspiring or established. Many examples and hundreds of problems are included, along with hints or complete solutions.
Lie Groups Beyond an Introduction, Hardback (August 2002)
Takes the reader from the end of introductory Lie group theory to the threshold of infinite-dimensional group representations. Merging algebra and analysis, this title uses Lie-theoretic methods to develop a theory having wide applications in mathematics and physics. It includes many problems, tables, and bibliographical notes.
Representation Theory of Semisimple Groups, Paperback (September 2001)
Offers a survey of representation theory of semisimple Lie groups. Suitable for both graduate students and researchers, this book states the theorems precisely, and gives many illustrative examples or classes of examples. It includes for the reader a useful 300-item bibliography and an extensive section of notes.
Cohomological Induction and Unitary Representations, Hardback (May 1995)» View all books by Anthony W. Knapp
Offers a systematic treatment of the development and use of cohomological induction to construct unitary representations. This book develops the necessary background in representation theory and includes an introductory chapter of motivation, a treatment of the "translation principle"ï¿½', and four appendices on algebra and analysis.
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