The special linear group for nonassociative rings

TL;DR

This paper generalizes the concept of the octonion special linear group to arbitrary rings, providing a Lie ring structure and explicit group computations, expanding the understanding of nonassociative algebraic groups.

Contribution

It extends Baez's definition of the octonion special linear group to all rings and describes the associated Lie rings over various classes of rings.

Findings

Computed all groups defined by Baez.

Described the Lie ring structure over associative rings and algebras.

Extended the definition to arbitrary rings.

Abstract

We extend to arbitrary rings a definition of the octonion special linear group due to Baez. At the infinitesimal level we get a Lie ring, which we describe over some large classes of rings, including all associative rings and all algebras over a field. As a corollary we compute all the groups Baez defined.