Splendid Morita equivalences for principal 2blocks with dihedral defect groups
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.
 Publication:

arXiv eprints
 Pub Date:
 December 2017
 arXiv:
 arXiv:1712.09274
 Bibcode:
 2017arXiv171209274K
 Keywords:

 Mathematics  Representation Theory;
 Mathematics  Group Theory;
 16D90;
 20C20 (Primary) 20C15;
 20C33 (Secondary)
 EPrint:
 To appear in Math. Z