Identifier

etd-03122010-131541

Degree

Doctor of Philosophy (PhD)

Department

Mathematics

Document Type

Dissertation

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.

Date

2010

Document Availability at the Time of Submission

Release the entire work immediately for access worldwide.

Committee Chair

Hoffman, Jerome

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