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The classification of the indecomposable liftable modules in blocks with cyclic defect groups
Author(s) -
Hiss Gerhard,
Naehrig Natalie
Publication year - 2012
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/blms/bds025
Subject(s) - indecomposable module , mathematics , algebraically closed field , pure mathematics , block (permutation group theory) , field (mathematics) , topology (electrical circuits) , discrete mathematics , combinatorics
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.