Local Representation Theory has 1 rating and 1 review. Steve said: This is a great book on modular representation theory, focusing on the basics J.L. Alperin. concise treatment of some topics from group theory and representation theory for a one term course. Authors: Alperin, J.L., Bell, Rowen B. Local Structure. Maybe I misunderstand your first question. The source is by definition a module of the vertex, namely the module M for which U | M G. Trivial source in this.
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Return to Book Page. Preview — Local Representation Theory by J. Representation theory has applications to number theory, combinatorics and many areas of algebra. The aim of this text is to present some of the key results in the representation theory of finite groups by concentrating on local representation theory, and emphasizing module theory throughout. Paperbackpages.
Local Representation Theory by Alperin, J L
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This book is not yet featured on Listopia. Apr 22, Steve Dalton rated it it was amazing Shelves: This is a great book on modular representation theory, focusing on the basics of the theory and how the projective, indecomposable, simple, etc.
The books main goal and the unifying theme of the last chapter is tueory the projective indecomposables over a block with cyclic defect group, which is essentially the only well-understood case in block theory, aside from a few exceptional cases.
The book is organized This is a great book on modular representation theory, focusing on the basics of the theory and how the projective, indecomposable, simple, etc.
The book is organized in an excellent way, going from the general to the specific, with each result being built upon the ones from the previous section s. The author also takes the time to explain what certain theorems are about, and why one might care; this was especially nice when the theiry became a little too much to process all qlperin once. Right then, the author would include a paragraph or two describing the important case to pay attention to, or the general “idea” of the theorem and how it is used.
Many key topics are treated here, with surprising clarity and conciseness, and just the right level of sophistication: The sections on the Wedderburn theorem and the Krull-Schmidt theorem are great, and the later sections on the Representatlon operator, the Green correspondence, and Brauer’s Main Theorems are all very clear.
The discussion in the last few sections on Brauer trees and graphs is also very insightful and well-done. There are a few complaints though. I find the exposition get a little too involved at points, going through lines of calculation that are easy to gloss over and I definitely did a few timesbut sometimes those calculations are the only way to go.
The notation also leaves a lot to be desired, but that’s characteristic of representation theory as a whole it seems.
My only real complaint – without a companion excuse – is that the rerpesentation are a little bit all over the place: Unfortunately, the only ones that get used later in the book are the dull, difficult ones. When I was thinking how many stars to give this book or any group theory bookI always compare to my favorite: Isaacs’s Finite Group Theory. This is an unfair comparison for most books: FGT is clear and engaging, with complete proofs that somehow avoid messy details; the exposition flows naturally and many times I would find myself thinking “of course!
Alperin’s book holds up on most fronts, except it is a little computational at points, but the explanations and writing style are truly top-notch. Nitin CR added it Mar 25, M marked loval as to-read Jun 27, Alexander Hulpke added it Oct 10, There are no discussion topics on this book yet. Trivia About Local Representat No trivia or quizzes yet. Just a moment while we sign you in to your Goodreads account.