On the Borel transgression in the fibration $G\rightarrow G/T$

TL;DR

This paper provides an explicit corrected formula for the Borel transgression in the fibration of a semisimple Lie group over its maximal torus, aiding in the computation of their integral cohomology rings.

Contribution

It offers a corrected and explicit formula for the Borel transgression in the fibration of semisimple Lie groups, improving previous results and enabling cohomology ring calculations.

Findings

Corrected an error in the Borel transgression formula

Derived an explicit formula for the transgression

Applied to compute integral cohomology rings of compact Lie groups

Abstract

Let $G$ be a semisimple Lie group with a maximal torus $T$. We present an explicit formula for the Borel transgression $\tau :H^{1}(T)\rightarrow H^{2}(G/T)$ of the fibration $G\rightarrow G/T$. This formula corrects an error in the paper \cite{K}, and has been applied to construct the integral cohomology rings of compact Lie groups in the sequel works \cite{D,DZ2}.