On realization of some twisted toroidal Lie algebras

TL;DR

This paper provides a new presentation for twisted toroidal Lie algebras of types A and D, extending the understanding of their structure beyond the untwisted cases.

Contribution

It introduces a presentation for twisted toroidal Lie algebras of types A and D, building on previous work for untwisted cases.

Findings

Presented a new algebraic presentation for twisted toroidal Lie algebras.

Extended the classification of toroidal Lie algebras to include twisted types A and D.

Enhanced the theoretical framework for studying these algebras.

Abstract

Toroidal Lie algebras are generalizations of affine Lie algebras. In 1990, Moody, Rao and Yokonuma gave a presentation for untwisted toroidal Lie algebras. In this paper we give a presentation for the twisted toroidal Lie algebras of type $A$ and $D$ constructed by Fu and Jiang.