The octonions form an Azumaya algebra in certain braided linear Gr-categories

TL;DR

This paper demonstrates that octonions can be viewed as Azumaya algebras within specific braided linear Gr-categories by interpreting them as twisted group algebras, expanding their algebraic understanding.

Contribution

It introduces a novel categorical perspective on octonions, showing they form Azumaya algebras in certain braided tensor categories, which is a new theoretical insight.

Findings

Octonions can be modeled as twisted group algebras.

They form Azumaya algebras in specific braided categories.

Provides a categorical framework for understanding octonions.

Abstract

By applying the idea of viewing the octonions as an associative algebra in certain tensor categories, or more precisely as a twisted group algebra by a 2-cochain, we show that the octonions form an Azumaya algebra in some suitable braided linear Gr-categories.