A characterization of hereditary categories with tilting object

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Triangle singularities, ADE-chains, and weighted projective lines (2012, background): “We further exhibit—on a still conjectural level—new spontaneous series of such algebras not covered by Happel-Seidel symmetry, see Section 6.3.”
Homological and Homotopical Aspects of Torsion Theories (2007, methodology): “For instance this generalized tilting process was used in an essential way in the classification of hereditary Noetherian abelian categories with Serre duality by Reiten-Van den Bergh in [89] and the classification of hereditary abelian categories with tilting object by Happel in [59].”
LECTURES ON HALL ALGEBRAS (2006, background): “ptic curve Xacts on DHCoh(X). This action turns out to be the key point in understanding the structure of the algebra DHCoh(X) (the elliptic Hall algebra studied in [BS1]). A recent theorem of Happel [Ha2] states that any (connected) hereditary category which is linear over an algebraically closed ﬁ”
Spectral analysis of finite dimensional algebras and singularities (2008, background): “The last assertion then follows from Happel’s trace formula (Proposition 1.2).”
A homological characterization of piecewise hereditary algebras (2008, methodology): “this situation have been described in [ 5 ]a nd [7], but we do not have to make use of these investigations.”