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Gale duality and Koszul duality

Braden, Tom; Licata, Anthony; Proudfoot, Nicholas; Webster, Ben

Description

Given a hyperplane arrangement in an affine space equipped with a linear functional, we define two finite-dimensional, noncommutative algebras, both of which are motivated by the geometry of hypertoric varieties. We show that these algebras are Koszul dual to each other, and that the roles of the two algebras are reversed by Gale duality. We also study the centers and representation categories of our algebras, which are in many ways analogous to integral blocks of category O.

CollectionsANU Research Publications
Date published: 2010
Type: Journal article
URI: http://hdl.handle.net/1885/79436
Source: Advances in Mathematics
DOI: 10.1016/j.aim.2010.04.011

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