FIXED POINT SUBALGEBRAS OF INVARIANT AFFINE REFLECTION ALGEBRAS

The class of invariant affine reflection algebras is the last and the most general known extension of the class of affine Kac-Moody Lie algebras, introduced in recent years. We study the subalgebra of fixed points of an invariant affine reflection algebra under certain finite order automorphisms. We show that this subalgebra is again an invariant affine reflection algebra. Also, we show that starting with an invariant affine reflection algebra (g; T) and a certain finite order automorphism ¾, (g; T0) is again an invariant affine reflection algebra, where T0 is the subspace of fixed points of ¾ in T.