A remark on Leclerc's Frobenius categories
Martin Kalck
TL;DR
This paper reveals that Leclerc's Frobenius categories can be described as Gorenstein projective modules over an Iwanaga-Gorenstein ring with virtual dimension at most two, linking cluster algebra structures to Gorenstein homological algebra.
Contribution
It provides a new characterization of Leclerc's Frobenius categories as Gorenstein projective modules over specific rings, based on a Morita type result.
Findings
Categories admit a Gorenstein projective module description
Ring has virtual dimension at most two
Connects Frobenius categories with Gorenstein homological algebra
Abstract
Leclerc recently studied certain Frobenius categories in connection with cluster algebra structures on coordinate rings of intersections of opposite Schubert cells. We show that these categories admit a description as Gorenstein projective modules over an Iwanaga-Gorenstein ring of virtual dimension at most two. This is based on a Morita type result for Frobenius categories.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.