Extended affinization of Invariant Affine Reflection Algebras

Invariant affine reflection algebras are the last and the most general known extension of affine Kac-Moody Lie algebras, introduced in recent years. We develop a method known as "affinization" to the class of invariant affine reflection algebras, and show that starting with an algebra from this class together with a certain finite order automorphism, and applying the so called "loop construction", we obtain again an invariant affine reflection algebra. This can be considered as an important step towards the realization of invariant affine reflection algebras.