Virginia Polytechnic Institute and State University
Representation theory of the diagram An over the ring k[[x]]
Abstract
dc:description.abstractFix R = k[[x]]. Let Q<sub>n</sub> be the category whose objects are ((M₁,...,M<sub>n</sub>),(f₁,...,f<sub>n-1</sub>)) where each M<sub>i</sub> is a free R-module and f<sub>i</sub>:M<sub>i</sub>⟶M<sub>i+1</sub> for each i=1,...,n-1, and in which the morphisms are the obvious ones. Let β<sub>n</sub> be the full subcategory of Ω<sub>n</sub> in which each map f<sub>i</sub> is a monomorphism whose cokernel is a torsion module. It is shown that there is a full dense functor Ω<sub>n</sub>⟶β<sub>n</sub>. If X is an object of β<sub>n</sub>, we say that X <u>diagonalizes</u> if X is isomorphic to a direct sum of objects ((M₁,...,M<sub>n</sub>),(f₁,...,f<sub>n-1</sub>)) in which each M<sub>i</sub> is of rank one. We establish an algorithm which diagonalizes any diagonalizable object X of β<sub>n</sub>, and which fails only in case X is not diagonalizable. Let Λ be an artin algebra of finite type. We prove that for a fixed C in mod(Λ) there are only finitely many modules A in mod(Λ) (up to isomorphism) for which a short exact sequence of the form 0⟶A⟶B⟶C⟶0 is indecomposable.
Degree
thesis:*- Name thesis:degree_name
- Ph. D.
- Level thesis:degree_level
- doctoral
- Discipline thesis:degree_discipline
- Mathematics
- Department dc:contributor.department
- Mathematics
- Grantor dc:publisher
- Virginia Polytechnic Institute and State University
- Year dc:date.issued
- 1986
Author and committee
dc:creator, dc:contributor.*- Author dc:creator
-
- Corwin, Stephen P.
- Chair dc:contributor.committeechair
-
- Green, Edward
- Committee members dc:contributor.committeemember
-
- Farkas, Daniel R.
- Wheeler, Robert
- Aull, Charles E.
- Brown, E.A.
Rights
dc:rights- Statement dc:rights
-
- In Copyright
- Licence dc:rights.uri
Identifiers
dc:identifier.*- Handle dc:identifier.uri
- http://hdl.handle.net/10919/50001
- OAI identifier oai:identifier
- oai:vtechworks.lib.vt.edu:10919/50001