Very general noncommutative projective planes do not admit phantom categories.
Ideal classes of three dimensional Sklyanin algebras
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abstract
In this paper we classify graded reflexive ideals, up to isomorphism and shift, in certain three dimensional Artin-Schelter regular algebras. This classification is similar to the classification of right ideals in the first Weyl algebra, a problem that was completely settled recently. The situation we consider is substantially more complicated however.
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Nonexistence of phantom categories on very general noncommutative projective planes
Very general noncommutative projective planes do not admit phantom categories.