Constructs non-rigid tensor-triangulated categories whose thick tensor-ideals form non-distributive lattices.
Ore's theorem for thick subcategories
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abstract
We characterize those finite groups for which the bounded derived category of finite dimensional representations over an algebraically closed field of characteristic $p$ has distributive lattice of thick subcategories: they are precisely the $p$-nilpotent groups. Along the way we give necessary and sufficient criteria for the bounded derived category and perfect complexes of a finite dimensional $k$-algebra to have distributive lattices of thick subcategories.
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Non-distributive lattices of thick tensor-ideals via trivial extensions
Constructs non-rigid tensor-triangulated categories whose thick tensor-ideals form non-distributive lattices.