I am interested in explicit formulae for the Casimir elements (or "Casimir operators") of low-dimensional, real, non-Abelian Lie algebras (d=2,3, and possibly 4). I am wondering if there is any reference with a list of, at least some, expressions for such Casimir elements. Even a few explicit expressions for some simple examples would be highly appreciated.

I know that there exist formal definitions and procedures, but, since those low-dimensional algebras are classified (e.g. https://en.wikipedia.org/wiki/Classification_of_low-dimensional_real_Lie_algebras) and well studied, I would like to avoid the whole construction of the enveloping algebra and the Casimir elements by hand. However, I could not find explicit formulae in the literature, since most books and lecture notes only give the general recipe and provide the typical example of $\mathfrak{su} (2)$.

Of course, if not a unique "list", also some references where I could retrieve different formulae for different cases would be a great answer!

Since I am a physicist, I apologise if my notation is unclear or imprecise. Thank you all in advance for any help.

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