A classification of involutive automorphisms of an affine Kac-Moody lie algebra

Abstract

AbstractIn this thesis we classify the conjugacy classes of involutions in Aut g, where g is an affine Kac-Moody Lie Algebra. We distinguish between two kinds of involutions, those which preserve the conjugacy class of a Borel subalgebra and those which don't.We give a complete and non-redundant list of representatives of involutions of the first kind and we compute their fixed points sets. We prove that any involution of the first kind has a conjugate which leaves invariant the components of the Gauss decomposition g = n− ⊕h⊕n+. We also give a complete list of representatives of the conjugacy classes of involutions of the second kind