Quasi-Hereditary Extension Algebras

By I. Ágoston, V. Dlab, E. Lukács. 2003

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Gradings on walled Brauer algebras and Khovanov’s arc algebra (2011, methodology): “ry algebra in the sense of [CPS], and the Vr,s(λ)’s are its graded standard modules. Moreover the resolution in (6) is a linear projective resolution, hence Kr,s(δ) is standard Koszul in the sense of [ADL]. Proof. The cellularity is deduced from [BS1, Theorem 4.4] in exactly the same way as [BS1, Co”
Highest weight categories arising from Khovanov's diagram algebra II: Koszulity (2008, methodology): “Therefore K� is Koszul by [ ADL , Theorem 1]. (Alternatively, this can be deduced from [CPS, Theorem (3.9)] and Corollary 5.5.) �”
Some homological properties of the category O (2007, background): “Then Ap is quasihereditary ([Rocha-Caridi 1980]) and inherits a positive grading Ap for A, with respect to which it is standard Koszul ([Beilinson et al. 1996; Ágoston et al. 2003]).”