Graphs and Noncommutative Koszul Algebras

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dc.contributor.authorHartman, Gregory Neilen
dc.contributor.committeechairGreen, Edward L.en
dc.contributor.committeememberParry, Charles J.en
dc.contributor.committeememberFarkas, Daniel R.en
dc.contributor.committeememberBrown, Ezra A.en
dc.contributor.committeememberLinnell, Peter A.en
dc.contributor.departmentMathematicsen
dc.date.accessioned2014-03-14T20:10:31Zen
dc.date.adate2002-04-25en
dc.date.available2014-03-14T20:10:31Zen
dc.date.issued2002-04-23en
dc.date.rdate2003-04-25en
dc.date.sdate2002-04-23en
dc.description.abstractA new connection between combinatorics and noncommutative algebra is established by relating a certain class of directed graphs to noncommutative Koszul algebras. The directed graphs in this class are called full graphs and are defined by a set of criteria on the edges. The structural properties of full graphs are studied as they relate to the edge criteria. A method is introduced for generating a Koszul algebra Lambda from a full graph G. The properties of Lambda are examined as they relate to the structure of G, with special attention being given to the construction of a projective resolution of certain semisimple Lambda-modules based on the structural properties of G. The characteristics of the Koszul algebra Lambda that is derived from the product of two full graphs G' and G' are studied as they relate to the properties of the Koszul algebras Lambda' and Lambda' derived from G' and G'.en
dc.description.degreePh. D.en
dc.identifier.otheretd-04232002-162108en
dc.identifier.sourceurlhttp://scholar.lib.vt.edu/theses/available/etd-04232002-162108/en
dc.identifier.urihttp://hdl.handle.net/10919/27156en
dc.publisherVirginia Techen
dc.relation.haspartdissertation.pdfen
dc.rightsIn Copyrighten
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/en
dc.subjectrepresentationsen
dc.subjectquiversen
dc.subjectKoszul algebrasen
dc.subjectdirected graphsen
dc.titleGraphs and Noncommutative Koszul Algebrasen
dc.typeDissertationen
thesis.degree.disciplineMathematicsen
thesis.degree.grantorVirginia Polytechnic Institute and State Universityen
thesis.degree.leveldoctoralen
thesis.degree.namePh. D.en

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