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 hyp...
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| Format: | Others |
| Language: | en |
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Virginia Tech
2014
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| Online Access: | http://hdl.handle.net/10919/39613 http://scholar.lib.vt.edu/theses/available/etd-10042006-143904/ |
| Summary: | 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. |
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