The classification of the indecomposable liftable modules in blocks with cyclic defect groups. (Q2918789)

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. Let \((K,R,k)\) be a \(p\)-modular system such that \(K\) has characteristic 0 and is large enough for \(G\). A \(kG\)-module \(X\) is said to be liftable over \(R\) if there exists an \(RG\)-lattice \(M\) such that \(X\cong k\otimes_RM\). The authors classify the indecomposable \(B\)-modules \(X\) which are liftable over \(R\). They use the description of the non-projective indecomposable \(B\)-modules given by paths in the Brauer tree associated to \(B\) [see \textit{G. J. Janusz}, Ann. Math. (2) 89, 209-241 (1969; Zbl 0197.02302)].