# Fermionic realization of twisted toroidal Lie algebras

## TL;DR

This paper develops a fermionic realization for twisted toroidal Lie algebras of specific types, utilizing a new algebraic presentation, which advances the understanding of their structure and representations.

## Contribution

It introduces a novel fermionic realization method for twisted toroidal Lie algebras based on a new algebraic presentation, expanding the tools for their analysis.

## Key findings

- Fermionic realization constructed for types A_{2n-1}, D_{n+1}, A_{2n}, D_4
- Utilizes Moody-Rao-Yokonuma-like presentation
- Enhances understanding of algebraic structure and representations

## Abstract

In this paper, we construct a fermionic realization of the twisted toroidal Lie algebra of type $A_{2n-1}, D_{n+1}, A_{2n}$ and $D_4$ based on the newly found Moody-Rao-Yokonuma-like presentation.