We found a match
Your institution may have access to this item. Find your institution then sign in to continue.
- Title
On exponents and Auslander-Reiten components of irreducible lattices.
- Authors
Jones, A.; Kawata, S.; Michler, G.O.
- Abstract
Let G be a finite group, and let R be a complete discrete rank one valuation ring of characteristic zero with maximal ideal $\max (R) = \pi R$ , and residue class field $R/\pi R$ of characteristic p > 0. The notion of the exponent of an RG-lattice L is due to J. F. Carlson and the first author [1]. In this note we use it to show that any non-projective absolutely irreducible RG-lattice L with indecomposable factor module $\bar {L} = L/\pi L$ lies at the end of its connected component $\Theta $ of the stable Auslander-Reiten quiver $\Gamma _s(RG)$ of the group ring RG. Since such lattices L belong to p-blocks B with non-trivial defect groups $\delta (B)$ we also study some relations between the order of $\delta (B)$ and the exponent exp( L).
- Publication
Archiv der Mathematik, 2001, Vol 76, Issue 2, p91
- ISSN
0003-889X
- Publication type
Article
- DOI
10.1007/s000130050547