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It happens that I stumbled on a class of infinite dimensional Lie algebras that are not Kac-Moody algebras and for which I was not really prepared for. I know some general results on infinite dimensional Lie algebras from Kac's first two chapters of his book. Is there any more comprehensive and up to date reference?

If possible I'm interested in an approach to infinite Lie algebras similar to the one of Kac (starting from Chevalley-Serre relations) and something not in the line of those suggested in this answer ( References: Infinite dimensional Lie algebras ).

In fact a review or a book that expands and deepens the first two chapters of Kac book without entering on Kac-Moody algebras would be optimal.

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    $\begingroup$ An approach to what? What are the kind of questions you're interested for an arbitrary Lie algebra? In which way are the Lie algebras given (by a presentation? as Lie algebras of vector fields? as graded Lie algebras with a law?...) This is overly broad. $\endgroup$
    – YCor
    Commented Sep 9, 2022 at 13:36
  • $\begingroup$ Sorry indeed, they are given a presentation. The approach Kac does in the first 2 chapters of his book "Infinite dimensional Lie algebras" is perfect. I just wanted to know some references that start where he finishes (regarding of course non Kac-Moody algebras) $\endgroup$
    – Dac0
    Commented Sep 9, 2022 at 17:24
  • $\begingroup$ @YCor sorry I saw I made an error in the question, now I've edited. Thank you! $\endgroup$
    – Dac0
    Commented Sep 9, 2022 at 17:26
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    $\begingroup$ I'd recommend anything written by Boris Feigin in last, ehhh, 40 years approximately. You'll find plenty of naturally occurring Lie algebras coming from solutions to Ising problem and boson-fermion correspondence. Papers that are older than arXiv can be found here mathnet.ru/php/person.phtml?option_lang=en&wshow=pubs_mnet&personid=20636 (unfortunately, only few of them are translated to English) $\endgroup$
    – Denis T
    Commented Sep 9, 2022 at 19:18

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