Venkatesh Rajendran "Root generated subalgebras of symmetrizable Kac-Moody algebras"

The derived algebra of a symmetrizible Kac-Moody algebra G is generated (as a Lie algebra) by its root spaces corresponding to real roots. In this paper, we address the natural reverse question: given any subset of real root vectors, is the Lie subalgebra of G generated by these again the derived algebra of a Kac-Moody algebra? We call such Lie subalgebras root generated, give an affirmative answer to the above question and show that there is a one-to-one correspondence between them, real closed subroot systems and π-systems contained in the positive system of G. Finally, we apply these identifications to all untwised affine types in order to classify symmetric regular subalgebras first introduced by Dynkin in the finite-dimensional setting. We show that any root generated subalgebra associated to a maximal real closed subroot system can be embedded into a unique maximal symmetric regular subalgebra. This is a joint work with Irfan Habib and Deniz Kus.