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The aim of this paper is to establish a connection between the standard Koszul and the quasi-Koszul property in the class of self-injective special biserial algebras. Furthermore, we give a characterization of standard Koszul symm...
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The aim of this paper is to establish a connection between the standard Koszul and the quasi-Koszul property in the class of self-injective special biserial algebras. Furthermore, we give a characterization of standard Koszul symmetric special biserial algebras in terms of quivers and relations.
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The paper generalizes some of our previous results on quasi-hereditary Koszul algebras to graded standardly stratified Koszul algebras. The main result states that the class of standardly stratified algebras for which the left sta...
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The paper generalizes some of our previous results on quasi-hereditary Koszul algebras to graded standardly stratified Koszul algebras. The main result states that the class of standardly stratified algebras for which the left standard modules as well as the right proper standard modules possess a linear projective resolution - the so called linearly stratified algebras - is closed under forming their Yoneda extension algebras. This is proved using the technique of Hilbert and Poincare series of the corresponding modules.
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We show that taking the wreath product of a quasi-hereditary algebra with the symmetric group inherits several homological properties of the original algebra, namely BGG duality, standard Koszulity, balancedness as well as a condi...
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We show that taking the wreath product of a quasi-hereditary algebra with the symmetric group inherits several homological properties of the original algebra, namely BGG duality, standard Koszulity, balancedness as well as a condition which makes the Ext-algebra of its standard modules a Koszul algebra.
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In this paper we define and study some quasi-hereditary covers for higher zigzag algebras of type A. We show how these algebras satisfy three different Koszul properties: they are Koszul in the classical sense, standard Koszul and...
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In this paper we define and study some quasi-hereditary covers for higher zigzag algebras of type A. We show how these algebras satisfy three different Koszul properties: they are Koszul in the classical sense, standard Koszul and Koszul with respect to the standard module Delta, according to the definition given in [24]. This last property gives rise to a well defined duality and we compute the Delta-Koszul dual as the path algebra of a quiver with relations. (C) 2020 Elsevier B.V. All rights reserved.
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We give necessary and sufficient conditions for zigzag algebras and certain generalizations of them to be (relative) cellular, quasi-hereditary or Koszul.
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We present an easily applicable sufficient condition for standard Koszul algebras to be Koszul with respect to δ. If a quasi-hereditary algebra δ is Koszul with respect to α, then δ and the Yoneda extension algebra of δ are K...
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We present an easily applicable sufficient condition for standard Koszul algebras to be Koszul with respect to δ. If a quasi-hereditary algebra δ is Koszul with respect to α, then δ and the Yoneda extension algebra of δ are Koszul dual in a sense explained below, implying in particular that their bounded derived categories of finitely generated graded modules are equivalent. We also prove that the extension algebra of δ is Koszul in the classical sense.
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Let A be a basic finite-dimensional k-algebra standardly stratified for a partial order ≤and Δ be the direct sum of all standard modules. In this article, we study the extension algebra of standard modules, characterize the stra...
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Let A be a basic finite-dimensional k-algebra standardly stratified for a partial order ≤and Δ be the direct sum of all standard modules. In this article, we study the extension algebra of standard modules, characterize the stratification property of Γ for ≤and ≤~(op), and obtain a sufficient condition for Γ to be a generalized Koszul algebra (in a sense which we define).
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Let A = circle plus i >= 0 A(i) be a piecewise-Koszul algebra with cohomology degree function delta(d)(p) such that d > p >= 2 and E(A) = circle plus(i >= 0) Ext(A)(i) (A(0), A(0)) its Yoneda algebra. We introduce a new grading on E(A):
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This is the second of a series of four papers studying various generalisations of Khovanov's diagram algebra. In this paper we develop the general theory of Khovanov's diagrammatically defined "projective functors" in our setting....
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This is the second of a series of four papers studying various generalisations of Khovanov's diagram algebra. In this paper we develop the general theory of Khovanov's diagrammatically defined "projective functors" in our setting. As an application, we give a direct proof of the fact that the quasi-hereditary covers of generalised Khovanov algebras are Koszul.
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We study the quadratic algebras in Artin-Schelter regular algebras of dimension 5 generated in degree 1 under the hypothesis that . All the algebras obtained are proved to be Koszul algebras or piecewise-Koszul algebras. In additi...
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We study the quadratic algebras in Artin-Schelter regular algebras of dimension 5 generated in degree 1 under the hypothesis that . All the algebras obtained are proved to be Koszul algebras or piecewise-Koszul algebras. In addition, we find that there don't exist d-Koszul (d > 2) Artin-Schelter regular algebras of dimension 5.
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