Mathematics > Representation Theory
arXiv:2606.21239 (math)
[Submitted on 19 Jun 2026]
Abstract:We investigate the structure of the poset of torsion classes for a finite dimensional algebra admitting a simple projective module. We generalise a result of Ladkani by showing that if two algebras are related by a 1-APR tilt, then their posets of torsion classes are related by a flip-flop. This implies that the incidence algebras of the posets are derived equivalent. We give two different proofs of this result. The first one applies to functorially finite torsion classes, and a key ingredient is to see the two posets we want to relate as subposets of a common poset of silting objects. The second proof applies to arbitrary torsion classes, and we use a similar strategy, this time embedding the two posets into a common poset of s-torsion pairs.
Submission history
From: Marius Goguet [view email]
[v1]
Fri, 19 Jun 2026 09:05:58 UTC (95 KB)
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