Electronic Resource
Springer
Archiv der Mathematik
75 (2000), S. 92-97
ISSN:
1420-8938
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
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 $(\pi )$ .
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/s000130050478
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