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31/01/2025 - The Joy of Lie Algebras, Part II: Representations, Modules and Lie's Theorem

In the previous blog post, we introduced the concept of Lie algebras and their related basic notions. We now proceed to investigate the theory of representations of Lie algebras.


The pictures used are from N.H. Abel's and A.-L. Cauchy's manuscripts. The one in the foothead is from Abel's proof that the division of a lemniscate into \(n\) equal parts by compass and straightedge is possible if and only if it can be done on a unit circle, linking to the theorem previously investigated by Gauss.