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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Isaacs’s Finite Group Theory.
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. Refresh and try again.
To see what your friends thought of this book, please sign up. 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.
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! This book is not yet featured on Listopia.
Local Representation Theory
My only real complaint – without a companion excuse – is that the exercises are a little bit thekry over the place: Return to Book Page. I suggest that we don’t misuse the comments for discussing a totally different question, since they are not at all suited for this purpose.
Goodreads helps you keep track of books you want to read. Paperbackpages. Many key topics are treated here, with surprising clarity and conciseness, and just the right level of sophistication: Now for representatioh second question.
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Local Representation Theory by Alperin, J L
From there, it is also easy to see that every indecomposable has a unique trivial submodule, and uniseriality follows. There are a few complaints though. Sign up using Facebook. If you can’t fill in the details in the above argument, feel free to open rfpresentation questions.
Trivia About Local Representat The discussion in the last few sections on Brauer trees and graphs is also very insightful and well-done. The author also takes the time to explain what certain theorems are about, and why one might care; this was especially nice when the details became a little too much to process all at once. Preview — Local Representation Theory by J. The aim of this text is to present some of the key results in the representation theory of finite groups representatiin concentrating on local representation theory, and emphasizing module theory throughout.
Apr 22, Steve Dalton rated it it was amazing Shelves: No trivia or quizzes yet. Email Required, but never shown. This is a great book on modular representation theory, focusing on the basics of the theory and how the projective, indecomposable, simple, etc.
Alperin “Local Representation Theory” Lemma – Mathematics Stack Exchange
The sections on the Wedderburn theorem and the Krull-Schmidt theorem are great, and the later sections on the Heller operator, the Green correspondence, and Brauer’s Main Theorems locxl all very clear. Alperin’s book holds up on most fronts, except it is a little computational at alpfrin, but the explanations and writing style are truly top-notch. Open Preview See a Problem? If you write out the definitions of these symbols, the implication becomes trivial, using transitivity of restriction: Nitin CR added it Mar 25, For those who don’t own the book the page is available on Google Books here.
One more quick question: Representation theory has applications to number theory, combinatorics and many areas of algebra.
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