Gale duality and Koszul duality

Tom Braden; Anthony Licata; Nicholas Proudfoot; Ben Webster

doi:10.1016/j.aim.2010.04.011

Gale duality and Koszul duality

Tom Braden^*, Anthony Licata, Nicholas Proudfoot, Ben Webster

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

32 Citations (Scopus)

Abstract

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.

Original language	English
Pages (from-to)	2002-2049
Number of pages	48
Journal	Advances in Mathematics
Volume	225
Issue number	4
DOIs	https://doi.org/10.1016/j.aim.2010.04.011
Publication status	Published - Nov 2010
Externally published	Yes

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abstract = "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.",

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AU - Proudfoot, Nicholas

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AB - 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.

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KW - Koszul duality

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JO - Advances in Mathematics

JF - Advances in Mathematics

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Gale duality and Koszul duality

Abstract

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