On centrality of even orthogonal $\mathrm K_2$

TL;DR

This paper provides a concise, uniform proof demonstrating the centrality of the K_2 group associated with simply-laced root systems of rank at least three, advancing understanding in algebraic K-theory.

Contribution

It introduces a new, streamlined proof of the centrality of K_2 for all simply-laced root systems of rank ≥3, simplifying previous approaches.

Findings

Proves centrality of K_2 for all simply-laced root systems of rank ≥3

Provides a uniform proof applicable to multiple root systems

Enhances theoretical understanding of algebraic K-theory

Abstract

We give a short uniform proof of centrality of $\mathrm K_2(\Phi,\,R)$ for all simply-laced root systems $\Phi$ of rank $\geq3$.