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In this paper, we prove that every standard Koszul (not necessarily graded) standardly stratified algebra is also Koszul. This generalizes a similar result of [3] on quasi-hereditary algebras.
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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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Let A be a standard Koszul standardly stratified algebra and X an A-module. The paper investigates conditions which imply that the module Ext* (A) (X) over the Yoneda extension algebra A* is filtered by standard modules. In partic...
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Let A be a standard Koszul standardly stratified algebra and X an A-module. The paper investigates conditions which imply that the module Ext* (A) (X) over the Yoneda extension algebra A* is filtered by standard modules. In particular, we prove that the Yoneda extension algebra of A is also standardly stratified. This is a generalization of similar results on quasi-hereditary and on graded standardly stratified algebras.
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This work concerns the moment map associated with the standard representation of a classical Lie algebra. For applications to deformation quantization it is desirable that , the coordinate algebra of the zero fibre of , be Koszul....
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This work concerns the moment map associated with the standard representation of a classical Lie algebra. For applications to deformation quantization it is desirable that , the coordinate algebra of the zero fibre of , be Koszul. The main result is that this algebra is not Koszul for the standard representation of , and of . This is deduced from a computation of the Betti numbers of as an S-module, which are of interest also from the point of view of commutative algebra.
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Given a finitely generated module M over a commutative local ring (or a standard graded k-algebra) (R, m, k), we detect its complexity in terms of numerical invariants coming from suitable m-stable filtrations M on M. We study the...
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Given a finitely generated module M over a commutative local ring (or a standard graded k-algebra) (R, m, k), we detect its complexity in terms of numerical invariants coming from suitable m-stable filtrations M on M. We study the Castelnuovo-Mumford regularity of gr(M)(M) and the linearity defect of M, denoted ld(R)(M), through a deep investigation based on the theory of standard bases. If M is a graded R-module, then reg(R)(gr(M)(M)) < infinity implies reg(R)(M) < infinity and the converse holds provided M is of homogenous type. An analogous result can be proved in the local case in terms of the linearity defect. Motivated by a positive answer in the graded case, we present for local rings a partial answer to a question raised by Herzog and Iyengar of whether ld(R)(k) < infinity implies R is Koszul.
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