Koszulity for semi-infinite highest weight categories
Thorsten Heidersdorf, Jonas Nehme, Catharina Stroppel
TL;DR
This paper proves that certain infinite highest weight categories with linear resolutions are Koszul, extending known results and applying them to Khovanov algebras and Deligne categories.
Contribution
It extends Koszulity results to infinite highest weight categories with linear resolutions, including applications to Khovanov algebras and Deligne categories.
Findings
Infinite highest weight categories with linear resolutions are Koszul.
Khovanov algebras are Koszul.
Representations of classical Deligne categories are Koszul.
Abstract
We show that any upper finite or essentially finite highest weight category where the standard objects have linear projective resolutions and the costandard objects have linear injective resolutions is Koszul. This extends the result of Agoston, Dlab, and Lukacs to the case of infinite highest weight categories. We apply this result to Khovanov algebras and representations of classical Deligne categories and show that these are Koszul.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Homotopy and Cohomology in Algebraic Topology · Advanced Operator Algebra Research