A Classification of some Quadratic Algebras

In this paper, for a select group of quadratic algebras, we investigate restrictions necessary on the generators of the ideal for the resulting algebra to be Koszul. Techniques include the use of Gröbner bases and development of Koszul resolutions. When the quadratic algebra is Koszul, we provide the associated linear resolution of the field. When not Koszul, we describe the maps of the resolution up to the instance of nonlinearity.

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

1998

Author dc:creator

• McGilvray, H. C.

Chair dc:contributor.committeechair

• Green, Edward L.

Committee members dc:contributor.committeemember

• Ball, Joseph A.
• Linnell, Peter A.
• McCoy, Robert A.
• Olin, Robert F.
• Yin, Ray

• Koszul algebra
• quadratic algebra
• monomial generators

Statement dc:rights

• In Copyright

Licence dc:rights.uri

• http://rightsstatements.org/vocab/InC/1.0/

Dc Identifier Other

etd-7598-162247

OAI identifier oai:identifier

oai:vtechworks.lib.vt.edu:10919/30699