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Descent of Equivalences and Character Bijections

Kessar, R. ORCID: 0000-0002-1893-4237 and Linckelmann, M. (2018). Descent of Equivalences and Character Bijections. In: Geometric and Topological Aspects of the Representation Theory of Finite Groups, PSSW 2016. Springer Proceedings in Mathematics & Statistics, 242. (pp. 181-212). Cham: Springer. ISBN 9783319940328

Abstract

Categorical equivalences between block algebras of finite groups—such as Morita and derived equivalences—are well known to induce character bijections which commute with the Galois groups of field extensions. This is the motivation for attempting to realise known Morita and derived equivalences over non-splitting fields. This article presents various results on the theme of descent to appropriate subfields and subrings. We start with the observation that perfect isometries induced by a virtual Morita equivalence induce isomorphisms of centres in non-split situations and explain connections with Navarro’s generalisation of the Alperin–McKay conjecture. We show that Rouquier’s splendid Rickard complex for blocks with cyclic defect groups descends to the non-split case. We also prove a descent theorem for Morita equivalences with endopermutation source.

Publication Type: Conference or Workshop Item (Paper)
Additional Information: This is a post-peer-review, pre-copyedit version of an article published in Carlson J., Iyengar S., Pevtsova J. (eds) Geometric and Topological Aspects of the Representation Theory of Finite Groups. PSSW 2016. Springer Proceedings in Mathematics & Statistics, vol 242. The final authenticated version is available online at: http://dx.doi.org/10.1007/978-3-319-94033-5_7
Subjects: Q Science > QA Mathematics
Departments: School of Mathematics, Computer Science & Engineering > Mathematics
URI: http://openaccess.city.ac.uk/id/eprint/21525
[img] Text - Accepted Version
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