The classification of the indecomposable liftable modules in blocks with cyclic defect groups

Let G be a finite group, let k be an algebraically closed field of positive characteristic p and let B be a block of kG with cyclic defect groups. We classify the indecomposable B‐modules which are liftable with respect to a splitting p‐modular system with residue class field k. The indecomposable n...

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Bibliographic Details
Published in:The Bulletin of the London Mathematical Society 2012-10, Vol.44 (5), p.974-980
Main Authors: Hiss, Gerhard, Naehrig, Natalie
Format: Article
Language:English
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Summary:Let G be a finite group, let k be an algebraically closed field of positive characteristic p and let B be a block of kG with cyclic defect groups. We classify the indecomposable B‐modules which are liftable with respect to a splitting p‐modular system with residue class field k. The indecomposable non‐projective modules in B are constructed from certain paths in the Brauer tree of B [G. J. Janusz, ‘Indecomposable modules for finite groups’, Ann. Math. 2 (1969) 209–224.]. We determine those paths that give rise to liftable modules. We also find the characters of the lifts of these modules.
ISSN:0024-6093
1469-2120
DOI:10.1112/blms/bds025