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Isomorphism between $\operatorname{End}_0(E)$ and $\operatorname{End}_0(E')$ as Lie algebra bundles

This may be a stupid question. I'm reading the paper "Automorphisms of moduli spaces of vector bundles over a curve" of Indranil Biswas, Tomas L. Gomez, V. Munoz (arXiv link). I have a ...
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