Group graded basic Morita equivalences and the Harris–Knörr correspondence
AbstractLet G be a finite group, let b be a G-invariant block with defect group Q of the normal subgroup H of G, and let {b^{\prime}\in Z(\mathcal{O}N_{H}(Q))} be the Brauer correspondent of b. We show that the bijection between the blocks of G covering b and the blocks of {N_{G}(Q)} covering {b^{\prime}}, induced by a {G/H}-graded basic Morita equivalence between the block extensions {b\mathcal{O}G} and {b^{\prime}\mathcal{O}N_{G}(Q)}, coincides with the Harris–Knörr correspondence.
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