Vogan Diagrams of Twisted Affine Kac-Moody Lie Algebras

TL;DR

This paper extends the theory of Vogan diagrams to almost compact real forms of twisted affine Kac-Moody Lie algebras, establishing a correspondence between diagram equivalence classes and algebra isomorphism classes.

Contribution

It develops the theory of Vogan diagrams for twisted affine Kac-Moody Lie algebras and proves their classification correspondence.

Findings

Equivalence classes of Vogan diagrams correspond to isomorphism classes of real forms.

The paper generalizes Vogan diagram theory to twisted affine Kac-Moody algebras.

Provides a classification framework for almost compact real forms.

Abstract

A Vogan diagram is a Dynkin diagram of a Kac-Moody Lie algebra of finite or affine type overlayed with additional structures. This paper develops the theory of Vogan diagrams for almost compact real forms of indecomposable twisted affine Kac- Moody Lie algebras and shows that equivalence classes of Vogan diagrams correspond to isomorphism classes of almost compact real forms of twisted affine Kac-Moody Lie algebras as given by H. Ben Messaoud and G. Rousseau.