Resolutions and cohomology of finite dimensional algebras

• Main Author: Bardzell, Michael
• Other Authors: Mathematics
• Format: Others
• Language: en
• Published: Virginia Tech 2014
• Subjects: Module; Ring; algebra; Cohomology; Quiver; LD5655.V856 1996.B373
• Online Access: http://hdl.handle.net/10919/39613; http://scholar.lib.vt.edu/theses/available/etd-10042006-143904/

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. === Ph. D.