Conjugation Theorem For Affine Kac-Moody Superalgebras

TL;DR

This paper extends a conjugacy theorem to affine Kac-Moody superalgebras, enhancing understanding of their structure and root space relations, with implications for their algebraic properties.

Contribution

It generalizes a key conjugacy theorem from Kac-Moody algebras to superalgebras and explores the structure of imaginary root spaces.

Findings

Extended conjugacy theorem to superalgebras

New relations in imaginary root spaces

Enhanced structural understanding of affine Kac-Moody superalgebras

Abstract

We extend a conjugacy Theorem of Cartan subalgebras, originally established for symmetrizable Kac-Moody algebras, to the broader context of affine Kac-Moody superalgebras. Along the way, we obtain several results that deepen our understanding of the structure of affine Kac-Moody superalgebras. Additionally, we achieve findings regarding the relations within the imaginary root spaces of symmetrizable affine Kac-Moody superalgebras, providing new insights into their algebraic properties.