Under a strong-source or strong-sink condition on maximal forbidden paths, gentle algebras satisfy hb.dim A ≤ 2·gl.dim A − 1 (or 2·f.dim A − 1), yielding a new quasi-tilted criterion when gl.dim A = 2.
[HL00] Fran¸ cois Huard and Shiping Liu
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Homological Bounds of Gentle algebras
Under a strong-source or strong-sink condition on maximal forbidden paths, gentle algebras satisfy hb.dim A ≤ 2·gl.dim A − 1 (or 2·f.dim A − 1), yielding a new quasi-tilted criterion when gl.dim A = 2.