While there is a number of good books on Kac-Moody algebras ("Infinite dimensional Lie algebras" by Kac is already enough), it seems to me there is lack of textbooks on Kac-Moody groups. nLab says that the standart textbook is "Kac-Moody groups, their flag varieties and representation theory" by Kumar, but I have certain concerns about this book, since some parts of it are copied from Kac's book almost word by word. For the first few chapters (which cover the basics of KM algebras theory) it is fine, since the original book is great, but I'm not sure about the rest and I couldn't find another source (other than papers). Any suggestions?
2026-05-06 05:20:34.1778044834
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What are the good textbooks on Kac-Moody groups?
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There is an introduction to minimal and maximal Kac-Moody groups (without proofs, but with several good references) in this PhD thesis - see chapters 5 and 6.
UPDATE: There is now a textbook entitled "An introduction to Kac-Moody groups over fields", published in the EMS Textbooks series.
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There is a book of Betrand Remy which has a chapter on buildings and Kac-Moody groups acting on it (chapter 11, here). Otherwise, almost all references are the ones you have already given - see for example the lecture Introduction to Kac-Moody groups and Lie algebras, by Prof. Perrin, at the Hausdorff centre in Bonn.