A mathematical structure for the generalization of the conventional algebra

TL;DR

This paper introduces a unified mathematical framework that generalizes conventional algebra using bijective functions, aiming to encompass various recent deformed algebras in generalized statistical theories for complex systems.

Contribution

It presents a novel algebraic structure that unifies multiple deformed algebras through the use of bijective functions, broadening the mathematical tools for complex statistical systems.

Findings

Any bijective function can be used to formulate a generalized algebra.

The framework unifies several recent deformed algebras.

Provides a mathematical basis for generalized statistical theories.

Abstract

An abstract mathematical framework is presented in this paper as a unification of several deformed or generalized algebra proposed recently in the context of generalized statistical theories intended to treat certain complex thermodynamic or statistical systems. It is shown that, from mathematical point of view, any bijective function can be used in principle to formulate an algebra in which the conventional algebraic rules are generalized.