Resolutions and cohomology of finite dimensional algebras
MetadataShow full item record
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.
- Doctoral Dissertations