ALPERIN LOCAL REPRESENTATION THEORY PDF

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Start your review of Local Representation Theory: Modular Representations as an Introduction to the Local Representation Theory of Finite Groups Write a review Shelves: math 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 studying 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 details became a little too much to process all at 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 reader still gets her hands dirty, but very rarely does she have to resort to mindless computation.

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 times , but sometimes those calculations are the only way to go.

My only real complaint - without a companion excuse - is that the exercises are a little bit all over the place: some are easy, some are difficult, some are interesting, and some seem very dull. Unfortunately, the only ones that get used later in the book are the dull, difficult ones. 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!

Highly recommended.

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Local Representation Theory

Home Questions Tags Users Unanswered. 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. Tgeory trivia or quizzes yet. Just a moment while we sign you in to your Goodreads account.

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