Locally isotropic Steinberg groups II. Schur multipliers

TL;DR

This paper calculates Schur multipliers for certain Steinberg groups with rank at least 3, establishing their well-definedness as abstract groups.

Contribution

It provides explicit computations of Schur multipliers for locally isotropic and root graded Steinberg groups of rank at least 3, excluding specific types.

Findings

Schur multipliers are computed for the specified Steinberg groups.

Locally isotropic Steinberg groups are shown to be well defined as abstract groups.

Abstract

We compute Schur multipliers of locally isotropic Steinberg groups and of all root graded Steinberg groups with root systems of rank at least $ 3 $ (excluding the types $ \mathsf H_3 $ and $ \mathsf H_4 $). As an application, we show that locally isotropic Steinberg groups are well defined as abstract groups.