A "q-deformed" generalization of the Hosszu-Gluskin theorem

TL;DR

This paper introduces a q-deformed generalization of the Hosszú-Gluskin theorem, expanding its framework using polyadic powers, diagrammatic language, and parameter q, with new invariance and homomorphism results.

Contribution

It presents a novel q-deformed version of the Hosszú-Gluskin theorem, including invariance and homomorphism formulations, extending the classical theorem's scope.

Findings

q-deformation parameter q can take special integer values

The q-deformed theorem maintains invariance properties

Examples illustrate the application of the q-deformed theorem

Abstract

In this paper a new form of the Hossz\'u-Gluskin theorem is presented in terms of polyadic powers and using the language of diagrams. It is shown that the Hossz\'u-Gluskin chain formula is not unique and can be generalized ("deformed") using a parameter q which takes special integer values. A version of the "q-deformed" analog of the Hossz\'u-Gluskin theorem in the form of an invariance is formulated, and some examples are considered. The "q-deformed" homomorphism theorem is also given.