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Author: D. J. Benson
Publisher: Cambridge University Press
Published: 1991-08-22
Total Pages: 296
ISBN-13: 9780521636520
DOWNLOAD EBOOK →A further introduction to modern developments in the representation theory of finite groups and associative algebras.
Author: D. J. Benson
Publisher: Cambridge University Press
Published: 1991-03-21
Total Pages: 260
ISBN-13: 9780521361347
DOWNLOAD EBOOK →This is the first of two volumes providing an introduction to modern developments in the representation theory of finite groups and associative algebras, which have transformed the subject into a study of categories of modules. Thus, Dr. Benson's unique perspective in this book incorporates homological algebra and the theory of representations of finite-dimensional algebras. This volume is primarily concerned with the exposition of the necessary background material, and the heart of the discussion is a lengthy introduction to the (Auslander-Reiten) representation theory of finite dimensional algebras, in which the techniques of quivers with relations and almost-split sequences are discussed in some detail.
Author: D. J. Benson
Publisher: Cambridge University Press
Published: 1998-06-18
Total Pages: 260
ISBN-13: 9780521636537
DOWNLOAD EBOOK →An introduction to modern developments in the representation theory of finite groups and associative algebras.
Author: D. J. Benson
Publisher:
Published: 2010-07-23
Total Pages:
ISBN-13: 9780521169905
DOWNLOAD EBOOK →Author: Kenneth S. Brown
Publisher: Springer Science & Business Media
Published: 2012-12-06
Total Pages: 318
ISBN-13: 1468493272
DOWNLOAD EBOOK →Aimed at second year graduate students, this text introduces them to cohomology theory (involving a rich interplay between algebra and topology) with a minimum of prerequisites. No homological algebra is assumed beyond what is normally learned in a first course in algebraic topology, and the basics of the subject, as well as exercises, are given prior to discussion of more specialized topics.
Author: Jon F. Carlson
Publisher: Springer Science & Business Media
Published: 2013-04-17
Total Pages: 782
ISBN-13: 9401702152
DOWNLOAD EBOOK →Group 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.
Author: D. Benson
Publisher: Springer
Published: 2008-07-22
Total Pages: 246
ISBN-13: 3540389407
DOWNLOAD EBOOK →This 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: Jens Carsten Jantzen
Publisher: American Mathematical Soc.
Published: 2003
Total Pages: 594
ISBN-13: 082184377X
DOWNLOAD EBOOK →Gives 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: Markus Linckelmann
Publisher: Cambridge University Press
Published: 2018-05-24
Total Pages: 523
ISBN-13: 1108562582
DOWNLOAD EBOOK →This is a comprehensive introduction to the modular representation theory of finite groups, with an emphasis on block theory. The two volumes take into account classical results and concepts as well as some of the modern developments in the area. Volume 1 introduces the broader context, starting with general properties of finite group algebras over commutative rings, moving on to some basics in character theory and the structure theory of algebras over complete discrete valuation rings. In Volume 2, blocks of finite group algebras over complete p-local rings take centre stage, and many key results which have not appeared in a book before are treated in detail. In order to illustrate the wide range of techniques in block theory, the book concludes with chapters classifying the source algebras of blocks with cyclic and Klein four defect groups, and relating these classifications to the open conjectures that drive block theory.
