Linear Algebraic Groups (Graduate Texts in Mathematics) by James E. Humphreys

Graduate Texts in Mathematics #21

by James E. Humphreys

James E. Humphreys is a distinguished Professor of Mathematics at the University of Massachusetts at Amherst. He has previously held posts at the University of Oregon and New York University. His main research interests include group theory and Lie algebras, and this graduate level text is an exceptionally well-written introduction to everything about linear algebraic groups.

Genres: Mathematics

Hardcover

First published May 13, 1975

Reviews

[Andrew · Rating 4 out of 5]

One of the satisfying things about reading Humphreys' books is the parsimonious approach he uses. Linear Algebraic Groups entirely avoids the use of scheme theory. Humphreys mentions in the preface that part of the motivation to write the textbook in the first place was the lack of an elementary treatment of the subject. The pitfall of this approach for many authors is that arguments can become convoluted in the absence of appropriate abstraction. But not here! The arguments Humphreys gives rarely feel like they are missing a deeper structure.

I might add that there is one very bad bump in the middle of the book which I found to be written in a confusing way (around chapter 20). This was the only section of the book where the pages were falling out of my library copy, presumably from students staring at it trying to make sense of it.

[Mikhail Ignatev · Rating 1 out of 5]

А вот как ни странно! Причина тому проста: семинар по этой книжке явно НЕ УДАЛСЯ!(( Сколь силён контраст с книжкой про алгебры Ли, очень, очень обидно. Возможно, конечно, дело в самом предмете или в моей тупости, но факт остаётся фактом - не идёт семинар, и всё тут. Печаль!( Совсем в первом приближении - пока добираешься до собственно алгебраических групп и их структуры, забываешь, ради чего всё затевалось.