# 2-local Baer correspondence

## Definition

The **2-local Baer correspondence** is a slight variation on the usual Baer correspondence that aims to establish a correspondence between things that *2-locally* look like Baer Lie rings and things that *2-locally* look like Baer Lie groups. Explicitly, it is a correspondence:

Baer alternating loop rings Baer diassociative loops

The correspondence:

Baer Lie rings Baer Lie groups

is a *sub*correspondence of this correspondence.

## Observations

The first thing we observe is that under this correspondence, it is possible for Lie rings that are not of class two (but have 2-local class two) to get mapped to diassociative loops that aren't groups. Conversely, it is possible for groups that are not of class two (but have 2-local class two) to get mapped to alternating rings that are not Lie rings.