Extended affinization of Invariant Affine Reflection Algebras

TL;DR

This paper extends the affinization process to invariant affine reflection algebras, enabling their construction via loop algebras and automorphisms, advancing their realization in Lie theory.

Contribution

It introduces a method to affinize invariant affine reflection algebras using loop constructions and automorphisms, broadening their structural understanding.

Findings

Established a loop construction method for invariant affine reflection algebras

Demonstrated that affinization preserves the algebra class

Provided a framework for realizing these algebras

Abstract

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.