Flexible idempotents in nonassociative algebras

TL;DR

This paper develops fusion rules for flexible power-associative algebras, introduces the concept of axes in a noncommutative context, and explores examples, advancing understanding of algebraic structures with idempotents.

Contribution

It extends fusion rule theory to noncommutative flexible power-associative algebras and defines axes in this setting, providing new insights and examples.

Findings

Fusion rules established for flexible power-associative algebras.

Introduction of axes in noncommutative algebraic setting.

Construction of noncommutative examples of these algebras.

Abstract

``Fusion rules'' are laws of multiplication among eigenspaces of an idempotent. We establish fusion rules for flexible power-associative algebras, following Albert. We define the notion of an axis in the noncommutative setting (compare with [HRS]) and accumulate information about pairs of axes. We also describe a class of noncommutative examples of flexible power-associative algebras.