I am doing self-study of affine Lie algebras, and while I have all recommended reference material, I find it hard to prepare for the exam.

It was quite easy to study finite-dimensional simple Lie algebras, as there are lots of exercises and solutions, as well as tutorials, available online.

This is the thing that I am missing for the case of affine Lie algebras; so far, I have seen very few exercise solutions, and it seems there are no online tutorials.

Question: Is there any book or online reference for exercises with solutions for affine Lie algebras?

In case of a printed book or an unsearchable PDF file, the referenced item can be in English, French, German, Russian, Spanish, or Italian.


1 Answer 1


You can find some exercises in the following lecture courses: http://www.maths.ed.ac.uk/~igordon/LA1.pdf (Infinite-dimensional Lie algebras, by Iain Gordon - no solutions are provided, though) http://www.math.uni-hamburg.de/home/runkel/Material/SS12/afflie-overview.pdf (by Ingo Runkel from this webpage http://www.math.uni-hamburg.de/home/runkel/ss12-affine.html )

In Russian there is Задачи семинара "Алгебры Ли и их приложения" by Парамонова И.М. and Шейнман О.К. but again the solutions are absent.

Many exercises are in the classic book "Infinite-Dimensional Lie Algebras" by Victor G. Kac. Although there are no solutions, the origin of many exercises are indicated and you can consult original papers in case of difficulty.

BookZZ has electronic versions of the last two books.


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