On standard Auslander-Reiten sequences for finite groups

Abstract.

Let G be a finite group and ${\cal O}$ a complete discrete valuation ring of characteristic zero with maximal ideal $(\pi )$ and residue field $k = {\cal O}/(\pi )$ of characteristic p > 0. Let S be a simple kG-module and Q _S a projective ${\cal O} G$-lattice such that $Q_S / \pi Q_S$ is a projective cover of S. We show that if S is liftable and Q _S belongs to a block of ${\cal O} G$ of infinite representation type, then the standard Auslander-Reiten sequence terminating in $\Omega ^{-1}S$ is a direct summand of the short exact sequence obtained from some Auslander-Reiten sequence of ${\cal O}G$-lattices by reducing each term mod $(\pi )$.