Parafermionic and Generalized Parafermionic Algebras

TL;DR

This paper explores the properties of parafermionic and generalized parafermionic algebras, establishing their algebraic structures and connections to oscillator algebras, contributing to the mathematical foundation of quantum algebra systems.

Contribution

It demonstrates that generalized parafermionic algebras are polynomial algebras and links ordinary parafermionic algebras to Arik-Coon oscillator algebras, revealing new algebraic relationships.

Findings

Generalized parafermionic algebras are polynomial algebras.

Ordinary parafermionic algebras are connected to Arik-Coon oscillator algebras.

The paper discusses the fundamental properties of these algebras.

Abstract

The general properties of the ordinary and generalized parafermionic algebras are discussed. The generalized parafermionic algebras are proved to be polynomial algebras. The ordinary parafermionic algebras are shown to be connected to the Arik-Coon oscillator algebras.