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Let $G$ be a finite simple group of Lie type and let $T$ be a maximal torusof $G$. It is well known that if the defining field of $G$ is large enough,then the normaliser of $T$ in $G$ is equal to the algebraic normaliser$N(G,T)$. We identify explicitly all the cases when $N_G(T)$ is not equal to$N(G,T).$

On algebraic normalisers of maximal tori in simple groups of Lie type