Title page for ETD etd-03122010-131541


Type of Document Dissertation
Author Hawwa, Fareed
Author's Email Address fhawwa1@lsu.edu, fth200@nyu.edu
URN etd-03122010-131541
Title Koszul Duality for Multigraded Algebras
Degree Doctor of Philosophy (Ph.D.)
Department Mathematics
Advisory Committee
Advisor Name Title
Hoffman, Jerome Committee Chair
Delzell, Charles Committee Member
Litherland, Richard Committee Member
Neubrander, Frank Committee Member
Perlis, Robert Committee Member
Chen, Jianhua Dean's Representative
Keywords
  • koszul duality
Date of Defense 2009-12-01
Availability unrestricted
Abstract
Classical Koszul duality sets up an adjoint pair of functors establishing an equivalence of categories. The equivalence is between the bounded derived category of complexes of graded modules over a graded algebra and the bounded derived category of complexes of graded modules over the quadratic dual graded algebra. This duality can be extended in many ways. We consider here two extensions: first we wish to allow a multigraded algebra, meaning that the algebra can be graded by any abelian group (not just the integers). Second, we will allow filtered algebras. In fact we are considering filtered quadratic algebras with an (internal) multigrading.
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