Regular subalgebras of affine Kac-Moody algebras
  We classify regular subalgebras of affine Kac-Moody algebras in terms of their root systems. In the process, we establish that a root system of a subalgebra is always an intersection of the root system of the algebra with a sublattice of its root lattice.   We also discuss applications to investigations of regular subalgebras of hyperbolic Kac-Moody algebras and conformally invariant subalgebras of affine Kac-Moody algebras. 
Anna Felikson, Alexander Retakh, Pavel Tumarkin