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

Let $G$ be a semisimple Lie group with a maximal torus $T$. We present an explicit formula for the Borel transgression $τ:H^{1}(T)\rightarrow H^{2}(G/T)$ 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}.

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