Quadratic algebra of square groups

TL;DR

This paper introduces a non-abelian tensor product within quadratic algebra, extending the symmetric monoidal structure of abelian groups to a non-abelian context while maintaining key algebraic properties.

Contribution

It demonstrates the possibility of extending the tensor product to non-abelian groups in quadratic algebra, preserving right exactness and balanced properties.

Findings

Established a non-abelian tensor product in quadratic algebra

Extended linear algebra concepts to a non-abelian setting

Maintained right exactness and balanced properties in the new tensor product

Abstract

There is a long-standing problem of algebra to extend the symmetric monoidal structure of abelian groups, given by the tensor product, to a non abelian setting. In this paper we show that such an extension is possible. Morover our non abelian tensor product remains even right exact and balanced. We describe the new non-abelian tensor product in the context of quadratic algebra which extends linear algebra.