Nonassociative cyclic algebras and the semiassociative Brauer monoid

TL;DR

This paper explores semiassociative algebras, especially generalized cyclic algebras, and their role within the semiassociative Brauer monoid, proposing potential generalizations in characteristic p including nonassociative differential algebras.

Contribution

It introduces a framework for semiassociative algebras related to cyclic algebras and discusses extending the Brauer monoid to include nonassociative differential algebras in characteristic p.

Findings

Identification of semiassociative algebra classes related to cyclic algebras

Analysis of their behavior in the semiassociative Brauer monoid

Proposal of a generalization including nonassociative differential algebras

Abstract

We look at classes of semiassociative algebras, with an emphasis on those that canonically generalize associative (generalized) cyclic algebras, and at their behaviour in the semiassociative Brauer monoid defined by Blachar, Haile, Matzri, Rein, and Vishne. A possible way to generalize this monoid in characteristic $p$ that includes nonassociative differential algebras is briefly considered.