Resolutions and cohomology of finite dimensional algebras

The purpose of this thesis is to develop machinery for calculating Hochschild cohomology groups of certain finite dimensional algebras. So let A be a finite dimensional quotient of a path algebra. A method of modeling the enveloping algebra Ae of A on a computer is presented. Adding the extra hypothesis that A is a monomial algebra, we construct a minimal projective resolution of A over A e. The syzygies for this resolution exhibit an alternating behavior which is explained by the construction of a special sequence of paths from the quiver of A. Finally, a technique for calculating Hochschild cohomology groups from these resolutions is presented. An important application involving an invariant characterization for a certain class of monomial algebras is also included.

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

1996

Author dc:creator

• Bardzell, Michael

Chair dc:contributor.committeechair

• Green, Edward L.

Committee members dc:contributor.committeemember

• Linnell, Peter A.
• Parry, Charles J.
• Thomson, James E.
• Ball, Joseph A.

• Module
• Ring
• algebra
• Cohomology
• Quiver

Statement dc:rights

• In Copyright

Licence dc:rights.uri

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

Language dc:language.iso

en

Dc Identifier Other

etd-10042006-143904

OAI identifier oai:identifier

oai:vtechworks.lib.vt.edu:10919/39613