Lie algebras of an affinization of a generalized Cartan matrix (Q1127966)

The author defines the affinized Lie algebra \(g_a(A^{[1]})\) of \(A^{[1]}\), a 1-fold affinization of a generalized Cartan matrix \(A\) of finite or affine type and proves that the affinized Lie algebra \(g_a (A^{[1]})\) and the radical free contragredient Lie algebra \(g_c (A^{[1]})\) are homomorphic images of a Lie algebra with finitely generated many kernels.