I was wondering what was known about $\mathfrak{sl}_2(\mathbb{Z})$ as a Lie algebra; in particular, what is known about its representation theory? I know of some texts which treat Lie algebras generally over rings, but I haven't seen any that specifically discuss this example. It would be wonderful if there existed some analogue of a Clebsch-Gordan decomposition for tensor products of $V_n$ (by which I mean the irreps in the complex case), even if they are no longer irreducible over $\mathbb{Z}$. Thank you very much!