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Ágoston, István; Dlab, Vlastimil; Lukács, Erzsébet

doi:10.1023/a:1022373620471

Cited by 39 publications

(12 citation statements)

References 9 publications

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“…Example 7.1. In [4], it was shown that the classes K 2 and K coincide when A is standard Koszul and quasi-hereditary. It was also shown that, in this context, the class K is closed under the operation ω.…”

Section: Examplesmentioning

confidence: 99%

“…In [2] and [4] Ágoston, Dlab and Lukács were looking for conditions which would imply that the Yoneda extension algebra of a quasi-hereditary algebra is again quasihereditary. They proved in [4] that a quasi-hereditary algebra which is standard Koszul, that is, its right and left standard modules have top projective resolutions, satisfies this property. They also showed that this homological duality respects the stratifying structure, i.e., the functor Ext * A maps standard A-modules to standard modules over the extension algebra.…”

Section: Introductionmentioning

confidence: 99%

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Stratified modules over an extension algebra

Lukács¹,

Magyar²

2017

Czech.Math.J.

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Section: Examplesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Stratified modules over an extension algebra

Lukács¹,

Magyar²

2017

Czech.Math.J.

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“…All of the Koszul algebras that we consider in this paper will be quasi-hereditary, where there is a strengthening of these ideas. Following [1], an algebra A is standard Koszul if it is a positively graded (split) quasi-hereditary algebra such that all of its standard and costandard modules have linear projective resolutions. By [1, Theorems 1 and 3], any standard Koszul algebra is Koszul and if A is standard Koszul then so is E(A).…”

Section: More Generally Ifmentioning

confidence: 99%

“…, t (ℓ) ) as a labelling of (the diagram of) µ, where t (r) is the restriction of t to µ (r) . In this way, we talk of the rows, columns and components of a tableau t. For example, 1 ) is a µ-tableau then define Shape(t) = µ, so that Shape(t (r) ) = µ (r) , for 1 ≤ r ≤ ℓ. If t −1 (k) = (r, c, l), then we set comp t (k) = l. A µ-tableau t is standard if its entries increase along the rows and down the columns of each component.…”

Section: Cyclotomic Quiver Hecke Algebras and Combinatoricsmentioning

confidence: 99%

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Quiver Schur algebras for linear quivers

Mathas

2015

Proceedings of the London Mathematical Society

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Abstract. We define a graded quasi-hereditary covering of the cyclotomic quiver Hecke algebras R Λ n of type A when e = 0 (the linear quiver) or e > n. We prove that these algebras are quasi-hereditary graded cellular algebras by giving explicit homogeneous bases for them. When e = 0 we show that the KLR grading on the quiver Hecke algebras is compatible with the Koszul grading on the blocks of parabolic category O Λ given by Backelin, building on the work of Beilinson, Ginzburg and Soergel. As a consequence, e = 0 our cyclotomic quiver Schur algebras are Koszul over fields of characteristic zero. Finally, we give an LLT-like algorithm for computing the graded decomposition numbers of the cyclotomic quiver Schur algebras in characteristic zero.

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Localization algebras and deformations of Koszul algebras

Braden

Licata

Phan

et al. 2011

Sel. Math. New Ser.

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Abstract. We show that the center of a flat graded deformation of a standard Koszul algebra A behaves in many ways like the torus-equivariant cohomology ring of an algebraic variety with finite fixed-point set. In particular, the center of A acts by characters on the deformed standard modules, providing a "localization map." We construct a universal graded deformation of A, and show that the spectrum of its center is supported on a certain arrangement of hyperplanes which is orthogonal to the arrangement coming from the algebra Koszul dual to A. This is an algebraic version of a duality discovered by Goresky and MacPherson between the equivariant cohomology rings of partial flag varieties and Springer fibers; we recover and generalize their result by showing that the center of the universal deformation for the ring governing a block of parabolic category O for gl n is isomorphic to the equivariant cohomology of a Spaltenstein variety. We also identify the center of the deformed version of the "category O" of a hyperplane arrangement (defined by the authors in a previous paper) with the equivariant cohomology of a hypertoric variety.

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Cited by 39 publications

References 9 publications

Stratified modules over an extension algebra

Stratified modules over an extension algebra

Quiver Schur algebras for linear quivers

Localization algebras and deformations of Koszul algebras

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