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arXiv · 1712.09274

Splendid Morita equivalences for principal 2-blocks with dihedral defect groups

Shigeo Koshitani·Caroline Lassueur
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Abstract

Given a dihedral $2$-group $P$ of order at least~8, we classify the splendid Morita equivalence classes of principal $2$-blocks with defect groups isomorphic to $P$. To this end we construct explicit stable equivalences of Morita type induced by specific Scott modules using Brauer indecomposability and gluing methods; we then determine when these stable equivalences are actually Morita equivalences, and hence automatically splendid Morita equivalences. Finally, we compute the generalised decomposition numbers in each case.

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Shigeo Koshitani, Caroline Lassueur. 2017-12-26. Splendid Morita equivalences for principal 2-blocks with dihedral defect groups. https://arxiv.org/abs/1712.09274

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