Abstract
dc:description.abstractA new connection between combinatorics and noncommutative algebra is established by relating a certain class of directed graphs to noncommutative Koszul algebras. The directed graphs in this class are called full graphs and are defined by a set of criteria on the edges. The structural properties of full graphs are studied as they relate to the edge criteria. A method is introduced for generating a Koszul algebra Lambda from a full graph G. The properties of Lambda are examined as they relate to the structure of G, with special attention being given to the construction of a projective resolution of certain semisimple Lambda-modules based on the structural properties of G. The characteristics of the Koszul algebra Lambda that is derived from the product of two full graphs G' and G' are studied as they relate to the properties of the Koszul algebras Lambda' and Lambda' derived from G' and G'.
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 Tech
- Year dc:date.issued
- 2002
Author and committee
dc:creator, dc:contributor.*- Author dc:creator
-
- Hartman, Gregory Neil
- Chair dc:contributor.committeechair
-
- Green, Edward L.
- Committee members dc:contributor.committeemember
-
- Parry, Charles J.
- Farkas, Daniel R.
- Brown, Ezra A.
- Linnell, Peter A.
Subjects
dc:subject × 4Rights
dc:rights- Statement dc:rights
-
- In Copyright
- Licence dc:rights.uri
Identifiers
dc:identifier.*- Dc Identifier Other
- etd-04232002-162108
- OAI identifier oai:identifier
- oai:vtechworks.lib.vt.edu:10919/27156