Classification of generalized Cartan matrices of hyperbolic type (Q1111683)

An indecomposable generalized Cartan matrix is said to be of hyperbolic (resp. strictly hyperbolic) type if it is of indefinite (i.e., not finite nor affine) type and any connected proper subdiagram of the corresponding Dynkin diagram is of finite or affine (resp. finite) type. This paper gives a list of all Dynkin diagrams corresponding to (not necessarily symmetrizable) hyperbolic matrices, which solves Exercise 4.4 in \textit{V. G. Kac}'s famous book [Infinite dimensional Lie algebras (Birkhäuser 1983; Zbl 0537.17001) (2nd ed. Cambridge 1985; Zbl 0574.17010)].