ON ALGEBRAS OF FINITE REPRESENTATION TYPE.
Final technical rept.,
OREGON UNIV EUGENE
Pagination or Media Count:
This paper launches a new attack on the Brauer-Thrall conjecture that bounded representation type implies finite representation type for algebras by showing the relevance of the structure of indecomposables of certain special types, namely the stable every maximal submodule is indecomposable, the costable having the dual property, and the stable-costable indecomposable modules having both properties. We give sufficient conditions on the structure of the stable resp. costable, stable-costable indecomposables in order that the algebra will have at most finitely many isomorphism classes of modules of any finite composition length. Turning our attention to quasifrobenius algebras with large kernels i.e., satisfying the condition that a nilpotent endomorphism of any indecomposable of finite length has large or essential kernel we give somewhat sharper conditions that bounded type implies finite type for these algebras and make a contribution toward an open question of Curtis and Jans. An algebra has large kernels in particular when every indecomposable has square-free socle, which was the main hypothesis of the cited paper of Curtis and Jans.
- Theoretical Mathematics