Unified products for alternative and pre-alternative algebras

TL;DR

This paper develops a unified theoretical framework for alternative and pre-alternative algebras, classifying their extending structures using non-abelian cohomology and deformation maps.

Contribution

It introduces a unified product approach and classifies extending structures of these algebras through cohomology and deformation theory.

Findings

Unified product theory for alternative and pre-alternative algebras

Classification of extending structures via non-abelian cohomology

Application of deformation map theory to algebra extensions

Abstract

The theory of unified product and extending structures for alternative and pre-alternative algebras are developed. It is proved that the extending structures of these algebras can be classified by using some non-abelian cohomology and deformation map theory.