Partial abelianization of free product of algebras

TL;DR

This paper explores a generalized form of abelianization called partial abelianization for associative algebras, focusing on free products and employing combinatorial, representation theoretic, and algebraic geometric methods.

Contribution

It introduces the concept of partial abelianization of free product algebras and applies advanced mathematical techniques to study its properties.

Findings

Partial abelianization generalizes classical abelianization.

The study provides new insights into algebraic structures relevant to quantum theories.

Methods developed can be applied to analyze algebraic and geometric properties of free products.

Abstract

In this article we consider partial abelianization of associative algebra with respect to a subalgebra. This notion is a generalization of usual abelianization of associative algebra and has an application in Quantum Mechanics and Quantum Information Theory. Using combinatorial methods, representation theory and algebraic geometry we study partial abelianization of free product of algebras in our work.