Fermionic realization of toroidal Lie algebras of classical types

TL;DR

This paper introduces a novel fermionic operator-based construction of toroidal Lie algebras of classical types, notably including symplectic affine algebras, expanding the algebraic toolkit for these structures.

Contribution

It provides the first fermionic realization of toroidal Lie algebras of classical types, especially symplectic affine algebras.

Findings

Fermionic operators successfully construct toroidal Lie algebras of classical types.

First fermionic realization of symplectic affine algebras.

Advances algebraic methods for studying toroidal Lie algebras.

Abstract

We use fermionic operators to construct toroidal Lie algebras of classical types, including in particular that of symplectic affine algebras, which is first realized by fermions.