Algebra notes


Please keep in mind that most of these texts have never been proofread. (One day I realized that proofreading my own proofs took me way more time than writing them, and sometimes even more time than finding them.) Should you find any mistakes or have any other remarks, I will be very glad to hear about them (my email address is A@B.com, where A = darijgrinberg and B = gmail).
Texts:
Notes taken in lectures:
Papers (publications and preprints):
Other writings:
Sidenotes to Michiel Hazewinkel: Witt vectors. Part 1:

Witt vectors reside somewhere on the crossroads between algebra, combinatorics and number theory. Hazewinkel's text is, in my opinion, a must-read for everyone interested in at least two of these fields. It also sheds light on the representation theory of symmetric groups, the theory of symmetric polynomials, Hopf algebras and λ-rings.

I tend to advise Hazewinkel's text to anyone interested in any of the subjects mentioned, due to its very vivid and explanatory writing style. (It was the main thing that made me study combinatorial algebra!) Unfortunately, a multitude of typos makes reading it harder than it should be. If you have troubles with understanding something in the text, the reason may be in this list of errata (plus a few remarks). (Here is a more complete collection of errata which I sent to the author; these include obvious spelling mistakes which won't hinder anyone at understanding the text.)
Warning: Don't take my list of errata at face value. They can contain false positives and wrong corrections.

Here are some sidenotes I have made. Usually, these contain proofs of assertions which are mentioned without proof in Hazewinkel's work. Some contain generalizations/extensions (however, it's mostly the cheap kind of generalization, that barely adds any new content). I have written them for myself to keep track of what's true and what isn't; unfortunately they aren't very readable... LaTeX sourcecode of the above.

Sidenotes to Pavel Etingof, Oleg Golberg, Sebastian Hensel, Tiankai Liu, Alex Schwendner, Dmitry Vaintrob, and Elena Yudovina: Introduction to representation theory:

Errata to David M. Goldschmidt: Group Characters, Symmetric Functions, and the Hecke Algebra. (Apparently currently inaccessible from the AMS site. Makeshift archive.org link.)
These might not be complete, as I am not done reading the third part of the book, but I am not planning to read further. (The strength of this book lies in its Part II.)
Warning: Don't take my list of errata at face value. They can contain false positives and wrong corrections.

Errata to Hanspeter Kraft and Claudio Procesi: Classical Invariant Theory - A Primer.
I have read all of this text in 2010 (except for parts of §7.7-7.8) and learnt a lot from it. I hope these errata make reading it somewhat easier.
Warning: Don't take my list of errata at face value. They can contain false positives and wrong corrections.

Errata to William Crawley-Boevey: Cohomology and Central Simple Algebras.
There was not much to correct here, so this is just for the sake of completeness.
Warning: Don't take my list of errata at face value. They can contain false positives and wrong corrections.

Errata to Dominique Manchon: Hopf algebras, from basics to applications to renormalization, version v2 (2006).
LaTeX sourcecode for what it's worth.
"Errata" in the wider meaning of this word; this includes alternative proofs which I found nicer than the ones given in the article.
I can recommend Manchon's exposition. It has also appeared in "Handbook of Algebra" volume 5 (edited by Hazewinkel), but I cannot say that the "Handbook of Algebra" version is better or worse than the arXiv one (none is a subset of another).
Warning: Don't take my list of errata at face value. They can contain false positives and wrong corrections.

Errata to Alexander E. Holroyd, Lionel Levine, Karola Mészáros, Yuval Peres, James Propp and David B. Wilson: Chip-Firing and Rotor-Routing on Directed Graphs, version v3 (2008).
LaTeX sourcecode for what it's worth.
There are only few real mistakes here (and they can be easily fixed, maybe with the exception of the one in the proof of Lemma 2.8). Most of this file are clarifications for some arguments which I found nontrivial to follow.
The Holroyd-Levine-Mészáros-Peres-Propp-Wilson article is an exposition of one of the most striking (in my opinion) modern developments in combinatorics.
Warning: Don't take my list of errata at face value. They can contain false positives and wrong corrections.

Errata to F. G. Friedlander, M. Joshi: Introduction to the theory of distributions (Google Books link).
Not quite algebra, but as long as I don't have an analysis page...
This is a list of mistakes I caught in the first chapters (mostly 1-5 and 7) of the text. The majority of these are typographical; only a few seem to actually be of mathematical nature.
Warning: Don't take my list of errata at face value. They can contain false positives and wrong corrections.
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Algebra notes

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Darij Grinberg