On standard Auslander-Reiten sequences for finite groups

Authors
Citation
S. Kawata, On standard Auslander-Reiten sequences for finite groups, ARCH MATH, 75(2), 2000, pp. 92-97
Citations number
10
Categorie Soggetti
Mathematics
Journal title
ARCHIV DER MATHEMATIK
ISSN journal
0003889X → ACNP
Volume
75
Issue
2
Year of publication
2000
Pages
92 - 97
Database
ISI
SICI code
0003-889X(20000801)75:2<92:OSASFF>2.0.ZU;2-U
Abstract
Let G be a finite group and C a complete discrete valuation ring of charact eristic zero with maximal ideal (pi) and residue field k = C/(pi) of charac teristic p > 0. Let S be a simple kc-module and Qs a projective C G-lattice such that Qs/pi Qs is a projective cover of S. We show that if S is liftab le and Qs belongs to a block of CC of infinite representation type, then th e standard Auslander-Reiten sequence terminating in Omega(-1)S is a direct summand of the: short exact sequence obtained from some Auslander-Reiten se quence of CG-lattices by reducing each term mod (pi).