Title page for ETD etd-04232002-162108


Type of Document Dissertation
Author Hartman, Gregory Neil
Author's Email Address ghartman@math.vt.edu
URN etd-04232002-162108
Title Graphs and Noncommutative Koszul Algebras
Degree PhD
Department Mathematics
Advisory Committee
Advisor Name Title
Green, Edward L. Committee Chair
Brown, Ezra A. Committee Member
Farkas, Daniel R. Committee Member
Linnell, Peter A. Committee Member
Parry, Charles J. Committee Member
Keywords
  • representations
  • quivers
  • Koszul algebras
  • directed graphs
Date of Defense 2002-04-23
Availability unrestricted
Abstract
A 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'.

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