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Author: D. J. Benson
Publisher: Cambridge University Press
Published: 1991-08-22
Total Pages: 296
ISBN-13: 9780521636520
DOWNLOAD EBOOKA further introduction to modern developments in the representation theory of finite groups and associative algebras.
Author: D. J. Benson
Publisher: Cambridge University Press
Published: 1998-06-18
Total Pages: 260
ISBN-13: 9780521636537
DOWNLOAD EBOOKAn introduction to modern developments in the representation theory of finite groups and associative algebras.
Author: Armand Borel
Publisher: American Mathematical Soc.
Published: 2013-11-21
Total Pages: 282
ISBN-13: 147041225X
DOWNLOAD EBOOKIt has been nearly twenty years since the first edition of this work. In the intervening years, there has been immense progress in the use of homological algebra to construct admissible representations and in the study of arithmetic groups. This second edition is a corrected and expanded version of the original, which was an important catalyst in the expansion of the field. Besides the fundamental material on cohomology and discrete subgroups present in the first edition, this edition also contains expositions of some of the most important developments of the last two decades.
Author: A. Bialynicki-Birula
Publisher: Springer Science & Business Media
Published: 2002-04-24
Total Pages: 256
ISBN-13: 9783540432111
DOWNLOAD EBOOKThis is the second volume of the new subseries "Invariant Theory and Algebraic Transformation Groups". The aim of the survey by A. Bialynicki-Birula is to present the main trends and achievements of research in the theory of quotients by actions of algebraic groups. This theory contains geometric invariant theory with various applications to problems of moduli theory. The contribution by J. Carrell treats the subject of torus actions on algebraic varieties, giving a detailed exposition of many of the cohomological results one obtains from having a torus action with fixed points. Many examples, such as toric varieties and flag varieties, are discussed in detail. W.M. McGovern studies the actions of a semisimple Lie or algebraic group on its Lie algebra via the adjoint action and on itself via conjugation. His contribution focuses primarily on nilpotent orbits that have found the widest application to representation theory in the last thirty-five years.
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.
Author: D. Benson
Publisher: Springer Science & Business Media
Published: 1984
Total Pages: 246
ISBN-13: 3540133895
DOWNLOAD EBOOKThis reprint of a 1983 Yale graduate course makes results in modular representation theory accessible to an audience ranging from second-year graduate students to established mathematicians. Following a review of background material, the lectures examine three closely connected topics in modular representation theory of finite groups: representations rings; almost split sequences and the Auslander-Reiten quiver; and complexity and cohomology varieties, which has become a major theme in representation theory.
Author: Alexander Zimmermann
Publisher: Springer
Published: 2014-08-15
Total Pages: 720
ISBN-13: 3319079689
DOWNLOAD EBOOKIntroducing the representation theory of groups and finite dimensional algebras, first studying basic non-commutative ring theory, this book covers the necessary background on elementary homological algebra and representations of groups up to block theory. It further discusses vertices, defect groups, Green and Brauer correspondences and Clifford theory. Whenever possible the statements are presented in a general setting for more general algebras, such as symmetric finite dimensional algebras over a field. Then, abelian and derived categories are introduced in detail and are used to explain stable module categories, as well as derived categories and their main invariants and links between them. Group theoretical applications of these theories are given – such as the structure of blocks of cyclic defect groups – whenever appropriate. Overall, many methods from the representation theory of algebras are introduced. Representation Theory assumes only the most basic knowledge of linear algebra, groups, rings and fields and guides the reader in the use of categorical equivalences in the representation theory of groups and algebras. As the book is based on lectures, it will be accessible to any graduate student in algebra and can be used for self-study as well as for classroom use.
Author: Jing-Song Huang
Publisher: Springer Science & Business Media
Published: 2007-05-27
Total Pages: 205
ISBN-13: 0817644938
DOWNLOAD EBOOKThis book presents a comprehensive treatment of important new ideas on Dirac operators and Dirac cohomology. Using Dirac operators as a unifying theme, the authors demonstrate how some of the most important results in representation theory fit together when viewed from this perspective. The book is an excellent contribution to the mathematical literature of representation theory, and this self-contained exposition offers a systematic examination and panoramic view of the subject. The material will be of interest to researchers and graduate students in representation theory, differential geometry, and physics.
Author: Grégory Berhuy
Publisher: Cambridge University Press
Published: 2010-09-09
Total Pages: 328
ISBN-13: 1139490885
DOWNLOAD EBOOKThis is the first detailed elementary introduction to Galois cohomology and its applications. The introductory section is self-contained and provides the basic results of the theory. Assuming only a minimal background in algebra, the main purpose of this book is to prepare graduate students and researchers for more advanced study.
Author: Jon F. Carlson
Publisher: Springer Science & Business Media
Published: 2013-04-17
Total Pages: 782
ISBN-13: 9401702152
DOWNLOAD EBOOKGroup cohomology has a rich history that goes back a century or more. Its origins are rooted in investigations of group theory and num ber theory, and it grew into an integral component of algebraic topology. In the last thirty years, group cohomology has developed a powerful con nection with finite group representations. Unlike the early applications which were primarily concerned with cohomology in low degrees, the in teractions with representation theory involve cohomology rings and the geometry of spectra over these rings. It is this connection to represen tation theory that we take as our primary motivation for this book. The book consists of two separate pieces. Chronologically, the first part was the computer calculations of the mod-2 cohomology rings of the groups whose orders divide 64. The ideas and the programs for the calculations were developed over the last 10 years. Several new features were added over the course of that time. We had originally planned to include only a brief introduction to the calculations. However, we were persuaded to produce a more substantial text that would include in greater detail the concepts that are the subject of the calculations and are the source of some of the motivating conjectures for the com putations. We have gathered together many of the results and ideas that are the focus of the calculations from throughout the mathematical literature.
