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arxiv: 0708.1287 · v1 · submitted 2007-08-09 · 🧮 math.RT

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Universal derived equivalences of posets of tilting modules

Sefi Ladkani
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classification 🧮 math.RT
keywords derivedmodulesposetstiltingcyclesequivalentorientedquivers
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We show that for two quivers without oriented cycles related by a BGP reflection, the posets of their tilting modules are related by a simple combinatorial construction, which we call flip-flop. We deduce that the posets of tilting modules of derived equivalent path algebras of quivers without oriented cycles are universally derived equivalent.

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  1. Flip of lattices

    math.CO 2026-05 unverdicted novelty 7.0

    Defines flips and mutations on posets and lattices, proves mutable lattices are semidistributive, establishes local mutability for type-A and type-B Cambrian lattices, and introduces Ordovician lattices via iterated m...